Whats the best way to clean a shag carpet? its an off-white 5x7 throw rug.?

Use a good carpet cleaner (like Woolite Carpet Cleaner) or you can mix up an oxy clean solution (this really works good too) after your rug is dry you can use a metal rake (like use use outside) and it will fluff up the fibers and make it look brand new

By far the fastest and easiest way to do a small carpet like that is to take it down to the local carwash and powerwash the snot out of it. works really good.

Take it down to your local laundry mat and put it in one of those oversized washers, use your regular laundry soap, and dry on low.