Here is a great starter project to try when attempting to learn Cadsoft Eagle. Make a simple breakout board for a SMD device.
For example, here I’m making a breakout for the SSOP-28 package with a .65mm pitch. This breakout will also accept SSOP-14, 16, 20 and 24 pin devices. I sent this design to OSPark for fabrication, and total cost for 3 PCBs, delivered was $7.80. To start out, you can easily copy a device from an existing library, or if you want to go all out, make a library part yourself.
Here is my post about Cadsoft Eagle tutorials.