Most PCB fabs require to send the Gerber files.
When exporting Gerber files, it is really quite easy.
Also I share a way to exporting the Gerber files from Eagle.
It should including 2 steps -
1. exporting Gerber files - choose RS274-X
2. exporting Drill files -excellon.cam
There is a share in - it shows the steps to genrate Gerber files from Eagle with PICs. which may be easier to understanding.
Refer link: http://www.instructables.com/id/Generate-Gerber-Files-From-EAGLE-File/
And also it is important to generate the full complete Gerber files.
that should include:
Copper layers - .cmp , .sol
Soldermask layers - . stc, .sts
Silkscreen layers - .plc, .pls
Drill layers - .txt
Outline layer - .dim
If you want to make stencil, then also need included stencil files , that is - .crc, .crs
Hope this information can be helpful.