You can change money easily at banks and money changers both of which are found at many locations round the city, though more are found in the centre. Exchange buy and sell rates for the Euro and US Dollar (and often Polish Zloty) are displayed outside, usually by red LED digital displays. The rates shown are usually the rate you get, and no commission is charged. To exchange amounts larger than €150 you need to present your passport. In banks you should queue at the cashier desk (касса).
Money changers tend to give better rates than banks. On Chernyakovsky St. (ul. Черняховского), leading from the Europe shopping centre past the Central Market towards the Amber Museum, you will find a number of money changers and banks.
Many ATMs will give cash advances on a credit card (e.g. Visa, Mastercard) with a limit of 5,000 or 7,500 rubles, depending on which bank owns the ATM.