Bought a dryer with 4 prong plug, wall outlet is typical 3 prong. Is there an adapter or can I wire in a 4 prong?

When you say "typical three prong" do you mean a 3 prong dryer outlet or a regular duplex receptacle-type outlet?

If it's a three prong dryer outlet, I believe you can replace the cord on the dryer with a 3 prong cord so it will fit the receptacle.
However, I'm not an electrician so someone will have to back me up.

The instsllation manual should show you how. On a 4 wire the ground is frame connected. On. 3 wire the neutral has the ground strap. If you use a 3 wire cord, reconnect the frame ground to the neutral lug.

Check the electrical specifications for the dryer just to make sure that the dryer is allowed to be placed on a three prong connector. If it is (I suspect it will be) then the electrical instructions will guide you through the process to change out the cord and properly modify the dryer.