How to shoot RAW with a Nikon D3100?

I have no clue, I can't figure it out!

It is all in your user manual

Your user manual has an index that lists RAW files

Look on page 64 as a start

You can also process them in the using the retouch menu on your camera.

Page 160

As i recall i think you need to press "i" before shooting but after focusing
Then choose the one on the right top corner, then a list will show up at the top will be RAW