I usually have no problem discovering inspiration for songs.
My head is full of lyrical ideas, song titles, and clever one liner lyrics.
I could pump out lyrics that make sense usually on the call of a melody and while i'm still a new writer i have the worst time figuring out the melodies to start. Can you all share with me some of your techniques.

If I remember correctly it was Willie Nelson that once sad the melody is in the words so why do i have such trouble with them?
think in your head as to how you want the song to sound like (just the lyrical parts) there you get a sense of whether the song goes high or low, then you put some random notes in and tweak it from there

electro-acoustic guitar player
(looking for band in or near rayleigh - essex - UK)
Learn some theory man. Listen to songs you like, analyze them and see what makes them good. Remember it's not just notes, its the rhythm, the dynamics, is there one dominant rhythm or is there a polyrhythm over the top? (e.g. RHCP - Raindance Maggie has that cowbell over the top, that's a polyrhythm.)

I've heard multiple ways people work so here's some stuff I've heard in interviews from famous musicians.

Anthony Kiedis - The whole band jam, he sings randomly over the top with whatever is in his head/written in front of him. He takes a recording of the jam home and writes his vocals to it.

Sting - Writes the title of a song first. Tells a story in a verse, then comes up with a Chorus which "brings it all together." Usually mumbles the melody, listens to it all back and writes words to the mumbling.

Tom Waits - Takes a dictaphone in to basement with him and just sings and writes lyrics. He finishes the complete song this way then goes back to do the chords. He said this way your playing isn't dictating the melody, you are adapting to it.

James Hetfield - Sings phonetically over the top (e.g. la la la la) whilst doing the music. Then writes lyrics to the phonetic melody.

Noel Gallagher - Sits down and "goes fishing" Plays his guitar and tries to make it happen. Sings randomly along and again records everything. Then he works at it. He also said redrafting is the key and claims there is 10 different versions to certain songs.

Ray Davies - Sits with an instrument and writes a song, again with something to record in to. To come up with parts he sometimes switches to piano rather than guitar and also tries to combine ideas with other ideas he has come up with.

John Lennon and Simon Neil - I've heard them say lyrics come to them when they try to sleep so keep a notebook next to your bed and jot it down. Again, a phone or something that can record sound would also be a good idea as the lyrics may come with a melody.

John Frusciante - Sits with a guitar, an art pad (a pad with no lines) and ink. He records to a mini disc player and does it line by line. He writes one line, records it, stops. Comes up with the 2nd, records it, stops. He repeats this till it's done then goes over it again with a redraft.

Burt Bacharach - Advised people to learn music theory and analyze their favourite songs. Also said the ability to write on proper sheet music was a great help as you can see things working together more clearly (e.g. harmonies etc)

I hope this was helpful man. I know all these things through watching/reading interviews and biographies. Ultimately, there's no right way. Just keep hammering at it and have something to record on to at all times. I've used every method said above and it's ever-changing. The trick is to keep at it and keep redrafting (in my opinion)