playing a simple melody
 

When we hear a simple melody, say like "Happy Birthday", we can replicate the series of notes we just heard with our voice.

For some of you experienced players, how is this done on a guitar? (For any good musician on any instrument)

Are you able to play a series of notes on a guitar because:

(1) You can quantify the intervals between each note which then tells you how far up/down the strings/frets you need to move?

Or ...

(2) You worked it out before (or someone showed you) and you just memorized it.

(2) is the way I do it but (1) is probably the way I should strive for. But what training do you need? I guess ear training, but how to go about it...

Am I correct that many of you good players are able to do (1)? And if so, how did you attain that skill?

The same way, I believe.
Once the melody is internalized, it's just a matter of finding the notes it corresponds to. As an example, I'm thinking of the time I figured out the national anthem. It's fairly easy to do so correctly.
The trick is to fill in all the right chords and harmonies, bass lines etc...and making it interesting to listen to. Guitar is good that way. Many possibilities.
But I think the answer to your question is that singing the melody is essential, and then "guitarizing" it. ;)

I will miss fretting a correct interval or two when the melody jumps around. Some keys are easier than others. Some neck locations are easier than others.

For example start the melody on the seventh fret of the fourth string. How much are you going to stay on the same string versus crossing over to other strings? Compare that to starting the melody on the open third string.
Same question, however:

First example is in the key of D and you are starting up the neck. Second example is in the key of C and in first positon chord territory.

I usually try to find chord support ASAP. The second example (key of C) I have readily available first position chords C, G, and F. Most of the notes of the melody fall right in the chords and the ones that don't are easy to get to (except perhaps the B note during the F chord). Not only does the melody play easier but you also get the harmony notes at the same time.

Someone playing lead with other players supplying the chords would likly have a different approach.

So how do you "guitarize" it? Yes, given enough time to mess around I guess you can eventually figure it out by guessing and experimenting. But I'm talking about being able to play it on the spot, the same way a child is able to sing a simple melody on the spot after hearing it a few times.

I just started ear training on Justin Guitar website and he talks about interval training... Being able to hear and quantify the distance between one note to the next. So I am thinking if you were really good at this, then this is how you can figure out things on the spot.

I'm thinking this is what I need to strive for, and wanted to know if others went through this kind of training.

I first find the root note. It can be any root note. I don't always remember a tune in the correct key. After finding a key it's just a matter of playing by ear. The scale starts from the root. Variations on the scale are done by ear. If it goes wrong I'm not beyond a bit of hunt and peck.

If it's important for you to have that skill, then by all means work on it. Any practice that heightens your ability to refine your ears, like interval training, is a plus.
Personally, I never felt the urge or need on guitar to be able to reproduce an internalized melody "on the spot", like you mention.
What I have at the start is a rough sketch, and then I work at filling in the background and fine print. For me, that takes time and reflection. More like hunt and peck, as Stanron mentioned.
Sounds like you have a different mind set on that, which is just as valid. The goal in the end is the same, to make good music worth listening to. :)

IMO, Translating Melody/tune to guitar riff by yourself is what makes one a musician vs a guitar player who reads them from tabs/online.
That's what my goal is and looks like it'll be a long term goal.

This sounds very similar to my approach with my instrumentals. Taking time with one of my own compositions is often required and I have no problem hunting and pecking! I find being able to hum/sing the melody in my head is helpful in getting it into my brain, but if I find something I think I might lose over night I'll record a little on my phone so I can sleep that night!
I'll use a little theory to help with knowing what I've gotten myself into.....and to find a bridge (instrumentals), but through practice and repetition, there's also a span of time where I'll focus on how a piece "wants" to be played. Phrasing, dynamics, my own mood and what I'm hoping to convey. Recording helps identify spots that might need a re-work. Recently I had a piece I worked on for 6 months......when I recorded it, I felt that the first section wasn't "musical" enough.......so more time went into the redo of that section......it's a process!

It's a natural process that happens automatically the more you play guitar - provided you actually listen to what you play!
It may take years (if you don't focus on the process particularly), but you end up internalizing the sounds of chords, the sounds of particular intervals.
Of course, if you focus and constantly test yourself, the process would be quicker. Play a note, sing it. Sing a note, find it on guitar. Play a chord, sing the notes in the chord one by one. Etc.

Quite simply, that's how you establish the link between the guitar and your ear. You can do it without singing - just listening closely to the differences between chords and intervals, characterising their individual qualities - but singing helps it feel organic, more personally connected to you. (And if you can't sing now, it will improve your singing too.)

I found Musical-U really helpful for a couple of months of interval training, but I had no musical training at all before, so I found their explanations very clear. Yes, number 1. I still can't do it all that quickly but, yes, I'm listening for intervals, major 3rd, minor 3rd to a 5th, etc, and I know how to make those intervals on guitar anywhere that I want to play, so it doesn't matter which key I start in. I'm not really naming the interval, just matching them to those shapes on the guitar as I go through the tune. Knowing that most melodies are built around a chord provides a short cut as soon as you know what chord it is, but if there were no chord, it would just be intervals. I'm not trying to match the pitch (I think that's what JonPR is describing); I'm just matching the intervals in whatever key I want to play. Since you sing, I'd highly recommend thinking of the layout of the fretboard and chords in solfege syllables. I've found that tremendously helpful and efficient.

Yes, not perfect pitch. I'll settle for getting close to relative pitch for now. And starting with Justin Guitar site, I am starting to see the shapes to the various intervals. Nothing I didn't know how to fret before, but being able to put the names to them is very helpful. To know "that's what that is". I've gotten through being able to identify 2nd (do-re), 3rd (do-mi), 4th (do-fa), 5th (do-so) on the first try so pretty encouraging, although these are pretty basic and I'm sure it will get more complicated. I'll check out Music-U as you mentioned.

IMHO you're way, WAY overthinking this! To play stuff by ear you need: 1) your ear, & 2) your guitar. And as mentioned, a very useful 3rd tool is your voice.
Probably the easiest & best way is to learn to sing a melody, then teach it to your guitar (as it were). How do you know if your guitar has it right? Your ear will tell you.
Just doing it is how you get good at it. Talking about it won't work. Just do it. Searching websites, trying to gather all the info you can, trying to left-brain it to death won't help much. Just do it. You can try to ear train intervals if you want, it probably won't hurt. Or you can spend that time figuring out real music, assuming that's what you want to play. Most players who are good at it got that way doing the latter. They just did it.
As you tackle more complex melodies and want to figure out other guitar parts, chords etc, start working with recordings and slow-down software.

I'm only speaking for myself here, not the OP, but "just do it" assumes a great deal of understanding about music that I just flat did not have and I never would have figured out in the time I have left on earth without some information. It seems to me that some people, when they talk about playing by ear, are really saying they listen to something over and over with the instrument in hand and try notes till they find the right ones and then remember what they "figured out". That's a different thing, imo, than knowing how to play a melody you hear because you know the intervals of the melody and also where those intervals are on the guitar. People who can really "play by ear" know how to play a piece without trial and error, as far as I can tell.

People who can also discern pitch are, I think, less common than people who can play the intervals, which is a fairly easily learned skill set.

Yes, one does need to just do it. And I think I've been doing that, although not nearly long enough compared to some of you guys. But knowing there is a science to it and applying it, can cut down on the amount of guessing and meandering that might otherwise happen, is what I am hoping for.

From previous posts I believe that you're successful at systematic learning and I understand that, being more a left-brain guy myself. In my 4+ decades of playing music, and my observations of many musicians, it's generally folks who have the least inhibitions and preconceived ideas about how to learn that take best to learning by ear. Doesn't mean they all have equal abilities; some are naturals, most (like me) have to work a lot more at it. I think a general definition of 'learning by ear' is very broad and includes the whole gamut from 'heard it once and can play it' to 'spent 2 weeks learning it bit by bit via trial and error'.

I've recently spent a bunch of time with a jam group of fiddlers, most of them had the same teacher. These are beginner/intermediate to intermediate fiddlers, mostly women, and every one of them has ear learning ability far above what I've encountered in the general guitar player population, especially below an advanced level. The fiddle teacher encourages ear learning from the get-go, slow jams in her classes and leads a monthly, open-to-the-public slow jam. Her students take it for granted that you should be able to learn that way. It's like learning to play fiddle - they work at it and get better. Start simple and work their way up, without 'a great deal of understanding about music' to begin with.

I also recently took an intermediate/advanced Irish repertoire class for melody instruments (fiddle for me), taught by a couple who host a very popular bi-weekly jam downtown. 4 tunes/week. Course material was recordings only - played on harp, pipes, penny whistle, accordion, occasionally fiddle or tenor banjo. Most of these advanced students had to work at learning these (sometime pretty intricate) Irish tunes. Bad news for me was, with playing in a bluegrass band and an occasional contra dance crew, I had far less band width for stuffing 4 tunes/week in my head than I figured. But the class was still fun!