The only two common ways to travel to Kragujevac and from it are by car and by bus. Kragujevac has no airport, private helicopter is not what we consider to be the common way, and a train should be excluded.
If one travel by car from Belgrade, there are two ways – picturesque stari put (old road), and autoput (the highway), which, although a bit longer, takes less time. It is needed about 90 to 110 minutes for the travel.
If the bus is to be picked, it is highly recommendable to avoid Autosaobracaj company. Probably the best choice is Kragujexpress company. They have three arrivals from Belgrade to Kragujevac (at 1:45 pm, 4:30 pm and 9 pm), and three arrivals from Kragujevac to Belgrade (at 7:30 am, 10:45 am and 6:30 pm), daily. They have good, comfortable buses, friendly stuff and the good will to allow small pets entering the bus and traveling without extra charge. A bus usually needs a bit less than 2 hours to reach the destination.
You have several Taxi companies, but the cheapest one is MEGA. But you have to be careful because there are many fake taxi companies with similar names like Megal, Meda, etc. You can make difference between fake and real MEGA in telephone number that they have on their cars. Number of Mega call center is 034/36-36-39 so that is safe way of choosing right company.
Open bus called "Butterfly" (because of butterfly design on its back) works during summer. It starts from the square called Kod krsta, and its destination is lake in Sumarice. It is good way to reach Sumarice on hot summer day, and opportunity to see some of Kragujevac.
There are many taxi companies in Kragujevac, and the most of them offer very cheap service. The best way is to phone call taxi, but it can easily be stopped on the street or find at many taxi stations all over the city.
Here are several telephone numbers: (034)363639, (034)305500, (034)362362…
I recomende a taxi since it is realy very cheap. There are a few different taxi services. The phone number below is for one of tham. I don't know much about bus services, but i saw quite big number of them crusing the city.