Carbon frames & mountain biking are not obvious partners. Rocks, roost and other obstacles on the trail could easily damage your pride and joy. Here are a few ways I have protected my bikes in the past.

Click on the gallery for further detail.

Some people use heli tape. Here I have used car body protector sheet, as it is thicker and comes in large sheets. I have covered the underside of my bike, plus any part that may get foot or cable rub. Make paper templates first (measure twice, cut once !)
DIY Aluminium Chain suck protection. I am particularly proud of this one. I have just used aluminium flashing together with double sided tape. I made paper templates and then cut flashing with tin snips.
More aluminium flashing on chainstay.
From underneath (notice clear wrap also)
BBG Bashguard to protect chainrings. These are sstrong, light and very cheap (about 20 USD).
DIY bashguard on downtube. This one is made from an old crud catcher. Now you can buy aftermarket ones, but when I made this 4 years ago they did not exist.