Calling an exterminator or professional in is always a good bet. If you decide to do it yourself, that is also an option. The trick to doing it yourself is killing the bugs you don't see.
Killing bed bugs you do see is easy. Pesticides are always an option, as is isopropyl alcohol. You can always just smash them too, as bed bugs are very fragile.
Any bedding suspected or known to be infected should be washed and dried thoroughly. Heat is the main concern when it comes to getting rid of bed bugs and their eggs. Thorough vacuuming is necessary, as is covering or enclosing a mattress or box springs in plastic or another similar cover.
If you live in an apartment, condominium, or other rented residence, notify the landlord or property manager. Pest control may be included already in your lease at no extra charge to you. Residents of attached units would love a heads up.