There are many ways to change your money in Costa Rica, though most of them only apply in big tourist areas like San Jose.If you're staying at an international hotel of 3-stars or more, you should be able to change your money at the front desk or concierge. The fees are generally reasonable, and it's very convenient.
Almost any bank can change your money, and do so with very reasonable fees and the most current, official exchange rate. This is a very good way, but banks work short hours, so can be a bit of a hassle.
The very best way to change your money is at the ATM. The odds that your debit card from back home will work in the corner ATM is very high. You'll likely pay about a $3 fee (or so) to your bank, but you'll get the absolutely exact, correct exchange rate, without a fee. It's cheap, it's easy, and you don't have to bring nearly as much cash with you, which can be dangerous in terms of losing your money to misplacement or theft.
Some tourist stores or restaurants may offer to change your money, but the rates they'll charge will be way beyond the market rate, and you may end up paying double or triple for your meal.
The worst way to change your money is through some dude on the street. Counterfeiting is uncommon, but unfair exchange rates and other scams are more likely. Worst of all, an unknown guy you just met on the street will know how much money you have, and if he isn't there to rob you, but his friends around the corner just may be.