Advice on going from rat's nest to routed PCB
One resource that I refer people to quite frequently is David Jones' PCB Design Tutorial.

Lots of good info on component placement, routing, tolerances, layers, etc...

Just to reiterate what others have said, and D. Jones says as well, it all starts with component placement.  Be willing to rip up, move components, start over, etc...  Don't get lazy or stubborn and try to force that round peg into a square hole.  If the routing becomes difficult, there is probably a way to move or rotate parts so that suddenly it becomes easier.