For me, inspiration comes throughout the day. Just when I'm doing things a thought will come into my head, e.g. a phrase I'll use as a lyric, or just when I'm sat listenning to a song, I'll hear melodies, harmonies and stuff that aren't nessecary there, but were created because of them. It's not really a case of me sitting down, secluding myself from the world and going "Okay,what am I feeling now?".
I rarely write the whole song down straight away. I might write down the lyrics and stuff, but my view is that, if I can play it back from memory then it's something special and worth while carrying on with - if I've forgotten it, than maybe it wasn't all the great. I'll admit I've lost one or two pretty interesting things, but I suspect they'll be conquered up at some later date, when I'm "washing the dishes".