I just simply loaded up an example project..
Take a look at the attached photos... since this is an example, all those crossed tracks look a little worrying... do i have to manually sort them out or will it take care of it for me?
Its been a while since I did this, but Eagle does have an autorouter
Do a search on Eagle Autorouter
e.g. Eagle Autorouter Tutorial
But its not the best autorouter in the world
Take a look at this one http://www.freerouting.net/index.php?page=eagle
It usually gets good reviews (its uses java)
Personally I rather route manually, eagles autorouter quite often turns my schematics in to spaghetti. It can create loads of unneeded vias and sometimes it won't even finish autorouting, while I can if I do it myself.
Must say I haven't used freerouting yet.
It may indeed look like a mess when you've just added components and... look at the PCB-screen.
To me it's like freestyle jigsaw puzzling, If you rotate that IC 90 degrees CW for example, it already becomes
a lot easier to route.
Eagle does a fine job of autorouting if you have a good layout to start.
If your parts placement is crap, the autorouter will struggle as much as you will.
You may have to add some GND vias to connect all the GND islands together if you don't have many thru hole pins.
Move parts around, rotate them 90 or 180 degrees, reassign pins to be used or how they are placed on connectors.
Add polygon around the outside of the board on both layers and Name them GND.
Edit:Net Classes and set default to 10 mil wide, 12 mil drill, 10 mil clearance.
Right click a power trace and under properties select Power for the width.
Let it autoroute after that, see how it turns out.
Add Power net that is 20 mil wide, 24 mil drill, 10 mil clearance.