Yes, you can. A very small drywall repair may only need a can of drywall compound or spackle, and some tools, while a medium repair or larger will require you to cut out the damaged drywall and insert a new piece, then finish (tape, mud, and sand) the edges so the seams blend in. The hardest part of any drywall repair is drywall finishing (also called mudding and taping), because drywall finishing is more of an art that takes a lot of experience to master. A great physical repair can look terrible if the drywall finishing isn't done well, so we recommend you use an experienced drywall contractor for the drywall finishing step, even if you tackle the rest of the repair. Due to this, for some people it just makes more sense to have a drywall company perform the entire repair.