Side to side wobble, fishtailing, is usually due to brace height being too low. Also caused by badly matched arrow spine and bad release as others have mentioned. I don't know what bow you're shooting, but make sure the brace height is in the range recommended by the bowyer.

Up and down wobble, porpoising, is almost always due to nock height being wrong.

If the tail of the arrow looks like it's making a circle, it's a combination of both fishtailing and porpoising. In that case, I like to take care of the porpoising first, then the fishtailing. It doesn't really matter which one you fix first, but always fix one problem at a time.