Better check with your state laws first. Some states flat ban possession of auto weapons, others require some form of state registration or licensing. Assuming everything is OK in your state, you have to do the Federal paperwork. The Federal $200 tax is a transfer tax, paid by either party when the gun is transferred. It is not a yearly license fee, as some think.
If you are a resident of the same state as the seller, you may not need a dealer, depending on state law, but you still have to submit the Federal form, which requires the signature of your state/local police chief or representative, and $200.
If you are buying out of state, you will have to have the gun sent to a Class III dealer in your state (check with one first), and he should take care of the Federal paperwork, and will charge you for doing so, just like any other interstate transfer. You will probably have to appear in person at the police HQ, either way.
Obviously, if you are a convicted criminal, fugitive, etc., it is a crime even to apply.
You may think of BATF as that evil monstrous agency that will harass you forever if you own an auto weapon. Actually, the Feds don't really care much as long as the law is obeyed. If you get the OK from your local folks, and the NCIC doesn't turn up anything, they cash your check, stick on the stamp (yes, it is actually a stamp) and back comes the form. Don't lose the form and stamp; they are proof that your ownership of the gun is legal.