Make a runny batter using beer or water as the liquid and GoldenDipt All-Purpose Batter (available in most grocery stores). Its ingredients are primarily corn flour, wheat flour, salt, and a little leavening, so you can whip up a batch from that if you prefer. Dip the SqueakyCheese pieces in the batter, make sure each piece is completely coated, drain a little, then roll them individually in breading (GoldenDipt All-Purpose Breading works great) and no, I don't have stock in GoldenDipt Corp.! but finely crushed breadcrumbs work, also. Store the coated cheese pieces in a plastic bag in the freezer (important!) for an hour or until you are ready to cook.
Heat cooking oil to deep-fry temperature. I don't have a thermometer, but my "Fry-Daddy" electric deep fryer is probably at 375°F. Drop the cheese pieces in hot oil for 2 to 3 minutes or to taste, then remove and drain on paper towels. If you did everything right, each piece should have a shell of cooked batter around soft insides. They should be cool enough to bite into in just a few seconds. Eat them while they're hot!
I like to dip them in ranch dressing or chip dip.