You will find taxis everywhere. You are unlikely to have many problems with them, but always agree on a price beforehand. They can do it on the meter, but then they will only take you the long way round. Ask local shopkeepers/bar staff/hotel employees on how much a good price is so you've got a clue.
You can also get a dolmuÅ literally means "squashed taxi", just so you know what to expect!, a minibus service that runs along most main roads and past major hotels. If you are traveling far then you will probably have to change, but there should be a direct one to downtown Side. Charging around 3TL, this is the cheapest way to travel. They have stops, but you can ask the driver to stop anywhere on route usually. A cheap fun way of traveling, used by locals and tourists alike, just be prepared to travel in very crowded conditions.