Figure out a melody in your head first. If you go far enough back, all music is evolved from speech, but compositionally it's much easier to treat the voice as a separate instrument as opposed to a method to get out words. The words will come in in stops and starts. Lyrics are also never final until you've played it so many times you forget that everyone else is still hearing words come out of your mouth.
That being said, I'll outline my method put as concretely and creatively as I can muster (Enjoy, it's a little long... lol):
Before I started in with music, etc., like most kids, I played with legos, tinker toys, did some puzzles, and played connect the dots.
Legos: I usually start with the "blocks of sound" that will eventually make up the instrumental (or basis thereof) portion of the song. Then I listen, and try to figure out what I feel emotionally from the song. Just looking for a direction really, and start thinking about where the melody will sit in the song. Basically you're just putting musical licks together that you like. Even if you don't realize it, you're laying the bottom most layer of what the words will eventually be.
Box of Tinker Toys: Now that you have big chunks of the legos put together, you can move on to the melody. Listen to the song, and find a melody line, and start planning the overall composition a bit. Find bits you like. These are tinker toys. You can take apart old projects, or steal/borrow a few from the kid next door. Just trying to find enough tinker toys make sure you'll have most of the ones you want when you need them. On top of your good beginnings to a solid little fort built of legos, start just sticking tinker toys in the crooks and cranny's to see if they'll stick, or if you can build the Legos around them some for support. And yes, tinker toys and legos are hard to connect, but you can make them work together, you just can't be a perfectionist about it.
1000 Piece Puzzle: I play through the song like a 1000 more times staring at my box of tinker toys, some of which I already half-ass bolted together and put back in the box, and some of which are just totally wedged into a mostly finished, but kind of formless Lego structure (Maybe a couple of tinker-beams are actually perpendicular and look like they're supposed to be there). Then I scribble down words, phrases, thoughts, until I have a super loose outline of maybe what the lyrics could be. Those, my friend, are puzzle pieces. Anyway, the whole point of trying to build up the scaffolding of tinker toys is so that it will at least probably hold the puzzle you're working on when you get further along with connecting the pieces. You're looking for the pieces that you can put together without knowing what the picture is, cause it's just a bunch of dots. Find any "edge pieces," and it gets easier. If you can figure out some pattern to your particular set of dots you might start to see what the picture is eventually going to be as well.
Connect the dots: At this point, your lego structure should be pretty much done. You may want to put on some of the cool beveled pieces here and there, or try to match up block colors, but you know what it looks like and swapping out a piece or two probably isn't gonna make or break it, you're really just making it look nice. The scaffolding is shaky, but you've been working on it while you got the outline and several big sections of the puzzle done. There's a few pieces missing, but you can maybe start connecting the dots into whatever pattern they seem to be. Do it in pencil though. To be clear, since I haven't explained this metaphor, connecting the dots is the meaning of the song. As the bottom layers start to actually look structurally sound, and maybe even work together in cool ways you didn't set up intentionally, you're done with the puzzle. There's a piece or two under the couch somewhere, whatever. Mom'll find it next time she vaccums back there. You're trying to make the dots work, and they're obviously some kind of four legged animal, but the face is really hard. You'll get it, it just takes time and maybe some extra-creative connections. You're pretty close already, and you're friends should already be kind of impressed... or worried about your mental health. Both are good, after all their sanity never got them an awesome, epic tower of juicy metaphorical meanings, lol.
I suppose my point here, is that first of all, it's a lot of work. Second of all, it takes a lot of time and tweaking. Thirdly, you have to work in layers and in little parts that become bigger parts, but you really can't do one layer at a time. Each layer has requirements from the layer above and/or below it, it kind of just has to evolve. The song will be fun if you have fun with your creation, it'll be serious if you're serious while you're working, etc. Seriously, even when you finish connecting the dots, you can always bust out some colored pencils and put some pizazz in the final picture.
For the record, I sometimes think it would be faster and less tiring to build a fort out of legos, make scaffolding on top of the fort with tinker toys to support a 1000 piece puzzle of dots that I'm going to make into the portrait of a puppy. My final word of advice though, is don't be too turned off if the puzzle turns out looking more like picture of a cat when you're done. It was obviously a cat the whole time, and you were too distracted by stupid little kids toys to realize it back when you were snapping together Legos.