You can get anywhere in Crimea by mini bus. You can also go by taxi. Prices vary; be prepared to haggle a fare as you will always find someone to do a deal with. Many private citizens also work as pseudo taxi drivers; sometimes it is difficult to tell. Taxis range from modern comfortable cars to 1950s gas powered Soviet cars!
Frequently while traveling in the country if you look like a foreigner for example with a backpack and you are standing on what passes as a 'major' road people will stop and ask if you want a ride... for a price. Fortunately that price usually amounts to only a few USD to go some very long distances.
The road system in Crimea, as well as most of the Ukraine, is in very poor repair; expect huge potholes. There is a very strict zero policy to drinking & driving. Police patrols are frequent as well as roadside checks for documents. The death toll on Ukraine's roads is very bad, you have been warned.
If you can afford it you could consider flying, a return flight Kiev <-> Simferopol with Ukraine International Airlines is about $100.