I left a component unconnected on the layout, and Eagle doesn't check for that, for some reason. So make sure there are no airwires when you are done.
jeez that's reassuring.
and really strange.
I think they do that so that you have the option to leave certain things off the board if you wanted to without it throwing errors. Like if you had a diode selector switch that was on the schematic but intended to be wired off-board, you could just leave those parts unconnected. In Eagle, if it's on the schematic, it will be in the layout file. So it's nice not to have to place something on the PCB.
Anyway thanks entirely to Forrest, I completed my first Eagle schematic today, and am now in the layout stage. I tried to do a ground and power pour first, and crashed and burned pretty badly on the layout. Doing the pours first is definitely not intuitive to me yet.
There's no right way. I just do better when I have less airwires to look at from the beginning. The best way to do that is to have the pours done before you start routing (or sometimes placing the parts).
You can also do multiple pours (or planes) on each side. For example, you might want to do two planes on the top side; one for +9v and one for VREF. Or you might want to have half a ground plane on top as well. Just draw two polygons and name the same as the net you want them to "attach" to (such as +9v, VA, VB, GND, whatever).
Take a look at the layout image for the Stutter Trem. There are actually three planes on top: +9v, VA, and a skinny little GND plane running down the middle to isolate the LFO from the audio. I did a similar setup for the STM as well, albeit a little less complicated.