Melodies are kind of like spiritual epiphanies.....they just sort of come. sometimes they come on top of an instrumental chord structure....and sometimes they just come in dreams or through the air. I personally find that I don't sit and compose melodies. they just sort of happen.

I have a muse. Most of the time I have no idea where the melodies come from, although the structures tend to be traditional and come from experience and training. They typically start from a frame of mind and that might determine whether the structure is in a major or minor key and then perhaps also the mood might determine whether I head into major 6ths etc or something more clean.

I sometimes mess around making new chords or version thereof if I need some new inspiration.

i'll tell ya. I think there are an infinite number of ways in which melodies come about. you really got to just..... listen, to be trite about it !! Sometimes, melodies just pop into your head after finding a cool chordal sequence, sometimes it happens on the first couple times playing the chords through, and sometimes you play the chord sequence over and over and over for what seems like ages....loving the transitions, until, like I said, it just pops into your head. I've got to agree w/ the other comments here also, very true. I also have found, especially when I first started composing (and then when composing w/ lyrics) that if you just start playing notes... ya know... just oodleing around the keyboard/ fretboard/ etc., some little note sequence sticks out, you start playing around w/ it, and before you know it you find a melody that'll perpetuate itself. It's like having to write an essay for school, the hardest part is writting those very first few sentences, but once you got 'em the rest is much easier. And just like writing an essay, of which before even thinking of writting the first sentence, you have all your research and outlines done, so w/ music the research/outline pertains the who/what/where/why/how the song is about (feeling/ intensity/ etc.). (and just a note too, chord structure doesn't always come first ) hope that helps ! good luck.

I sing- a lot of the melodies I've ended using come when I've been in the bathtub. Maybe you should take a bath. i've made some of my best songs in the bath. I just sort of hear it in my head and then give voice to it and play with it, different variations, no words, just singing whatever sounds good. i don't currently play any instruments, so that's how i do it. Did you ever hear a really beautiful song in your head before and then realize you'd never heard it before that moment? Those are definitely melodies you can use. I hope that can help you.

Steal. Sort of. Learn all the melodies you can. Then learn them backwards. No joke. Keep them in the concious part of your brain. Sing them to yourself when you're supposed to be concentrating on the task at hand. They will make baby melodies with eachother. Ravi Shankar's "Kafi Holi" mates with a 14th Century Italian thing and a slimy newborn melody is born while you are playing that cool guitar part you've had for years that just needed a melody. Learn solfege - do re mi's and such. It's the language of melody. Best thing I ever did as a musician.