Ok, say I buy a new gun from a dealer. Do I pay the Federal Excise Tax, or does the dealer or manufacturer pick it up? In other words, is it added to the price later (like sales tax), or is it included in a dealer's price?

IIRC, the manufacturer pays it.

The way I understand it (and I'm sure someone will correct me if I'm wrong) is that it's already included in the price you pay.

If you buy a gun that was fully assembled from the manufacturer, it would have been paid by the manufacturer.

If someone else "manufactures" the gun (ie, putting a lower receiver and kit together) they pay the tax.

If you buy a kit and lower receiver from the same dealer, they're supposed to collect the tax, which is why many companies that sell parts and lowers will tell you they don't want to sell both at the same time since that means they have to deal with the FET.

If you buy a lower from one dealer and kit from another, you're the manufacturer and as long as you're not in the business of doing that, you don't pay the FET at all.