Transactions can be processed without fees, but trying to send free transactions can require waiting days or weeks. Although fees may increase over time, normal fees currently only cost a tiny amount. By default, all Bitcoin wallets listed on Bitcoin.org add what they think is an appropriate fee to your transactions; most of those wallets will also give you chance to review the fee before sending the transaction.
Transaction fees are used as a protection against users sending transactions to overload the network and as a way to pay miners for their work helping to secure the network. The precise manner in which fees work is still being developed and will change over time. Because the fee is not related to the amount of bitcoins being sent, it may seem extremely low or unfairly high. Instead, the fee is relative to the number of bytes in the transaction, so using multisig or spending multiple previously-received amounts may cost more than simpler transactions. If your activity follows the pattern of conventional transactions, you won't have to pay unusually high fees.
