The best way is to check with a local dealer FIRST. He can tell you if your CLEO will sign off and what steps you will need to take next. I doubt a dealer would let you pay for something he knows you won't be able to have, but it could happen, especially if he is not from your city/county.
You can also contact the CLEO's office directly, but dealers usually know the ropes and the people to contact.
Then, study catalogs, find what you want and make your deal. Dealers may want all the money or a big chunk of it up front, but most will return it if the CLEO/ATF business falls through. When the purchase money changes hands is of no concern to ATF, but ATF has to have the tax money with the application.
Jim