Buyer's Premium is a charge added to the hammer price (winning bid) of an auction lot. Buyer's premiums are typically set as a percentage of the winning bid, with a cap for higher priced items. Each auction is different, so look for the specific cost when you register.
Typically it is a very simple calculation. If there is a 20% buyer's premium and you win a lot for $100, your total price will be $120 + tax.
Unless you are tax exempt you will have to pay tax on the total of the sale price and buyer's premium combined. Maryland tax is 6%.
Use the demo calculator here to see how buyer's premiums and taxes could affect the final amount you would pay.