Buses go most everywhere in Turkey. They arrive at and leave from popular destinations very frequently. For most of your travel, this will be the way to get around. Exceptions would be the nice overnight trains between İstanbul and Ankara, İstanbul and Denizli, Adana and Ankara, and a few other routes.
They can travel fairly fast, although be aware that the travel times listed in guide books are sometimes a bit optimistic. Don't overlook the time spent waiting for the bus to leave, and the huge difference in travel time between a true ekspres bus and one that stops several times along the way.
Start by going to the otogar, or bus station. This may be a modern facility almost like an airport, like this otogar in Antalya.
Or it may be a simpler facility, like the otogar in Denizli.
Sometimes it's an array of shops and bus station offices, as in Göreme.
The long-haul buses are very nice rides.
The yardımcı, or attendant, will probably serve tea, soft drinks, and cold water, using a tiny "kitchen" in the stairwell.
The yardımcı will definitely bring around some lemon cologne. Buy a bottle for yourself to relive the experience!
The Ottoman Turks used rose water, first distilled in Arabia in the ninth century. Then "Eau de Cologne" or simply "cologne" reached the Ottoman Empire during the reign of Abdülhamit II (1876-1909) and became quite popular. Turkish businessmen started producing it, using rosemary, orange, bergamot (the oil that flavors Earl Grey tea), and of course lemon.
If you are going to a smaller town, or on a shorter trip, you may take a minibus like these in Denizli, above
Or, for short trips, a dolmuş like these below, parked in Göreme and seen from inside: