One of things I did the first year with almost every song I worked on by ear was to listen to Youtube versions of the song in phrase bites until i learned it the way Mike described. I memorized the rhythmic pattern's by memorizing the lyrics and using them as markers. Once you can feel the changes in the harmony and what the accents and groupings are in the rhythmic patterns, you need to have enough theory to understand which tones in the melody are basic chord tones (triads or dominants} and which are color tones because you can voice even basic progressions in a variety of ways. I agree with Mike, most songs, and almost always the simple ones {and I started with simplest songs} start and end on the tonic chord, so If you can get the key right away, it's much easier to pick out the melody and recognize the harmonies.

Then, you need basic chord theory to know when to change the chord because the melody moves to note that is no longer in the tonic chord -- which chords harmonize with the new note. its trickier than this, however, because the new note must be of long enough duration to warrant the change in harmony {not just be a passing tone, preparation, or anticipation tone, etc. to add interest and color}. A feeling for the lyrical phrasing, it's rhythm and cadences and which words in the lyric mark these is key to this process. You get this by listening to a lot of songs and trying to imitate their sounds. After doing this for a while, you know immediately which notes in the melody give a feeling outside the major harmonies, ie. wistful, dreamlike, tense, sad, etc. .
These are the unstable tones in a harmony that need to be resolved and which notes don't, and which are even more unstable because they go outside the diatonic scale {chromatics}, etc..

You also need to know when the harmony moves to an unstable chord even as it resolves to a stable tone in the key, because sometimes the chromaticism is not reflected in the melody. For instance, you can have a very simple tune like Blue Christmas based on the simplest of progression, the I V throughout, but it resorts to secondary dominants to keep it interesting, which means it goes out of the key and uses different chords even though they have the same harmonic functional relationship in another key. Therefore, recognizing the sound of certain chord progressions and the feeling you get from it is key (pun intended). So, start learning to recognize the stable and unstable aspects of these in the I V or I IV or IV V and their reversed orders.

After this, you can move beyond simple major tonalities and learn to recognize harmonies based on minor, modal and blues scales. All it takes is a lot of listening and a little bit of theory.

indeed, if it's an old standard that i can sing, i simply adopt a key, and sing along until i hear the first chord change. Granted, the chord progression isn't the melody, but the melody can be many times, within the chord tones. Some ragtime tunes that use a 'round the horn or circle or fifths motif. I'm lazy. I'll glean the chords from one of the many websites, but never trust them to be accurate. The most valuable tool, i use, is to have a good "model" of the song in my head. By the time it's ready for public consumption, it's pretty well ingrained. That's probably why i can't learn a tune i don't like.

I can already play a little bit by ear. I can memorize music extremely easy, usually only need to play something from sheet music once or twice and I never need to look at the sheets again. I've found that often times, I'm correcting mistakes by ear, or just playing simpler parts of the song by ear by just seeing the first few notes on sheets.

I don't really know how I'm doing it though, I just...do it I guess. I really want to buckle down and get better at it though. I actually struggle quite a bit with sheet music. I can read it, but it takes me a bit to really figure out what to play from it, and sightreading is out of the question at this point, lol.

Anyone have any experience with this?