Public transportation is quite readily available in the cities of Ghana. You can travel along the major inter-city route which stays quite crowded.
You can also travel around by TroTro which are privately owned vehicles carrying 10 to 20 passengers at a time and are found in abundance in Accra, the capital city of Ghana.
Trotro provides a connection to many cities. Like shared taxis, they run along fixed routes and have fixed fares. Chat with the locals using this mode of transport or you may opt for Okada, the motorcycle taxis of Ghana, popular transport choice in rural locations.
Roads throughout Africa are not in very good condition generally but Ghana has better.
Additionally, there are government-owned STC buses that commute between major cities.
For daily or multi-day traveling you can negotiate to charter a taxi or rental car which is generally available with the driver.