Hitchhiking in Ukraine is not very common. You could see occasional hitchhikers along the main roads and at gas stations with names of towns where they are heading written on pieces of cardboard and stretched out hands. In the countryside farmers' trucks would often be a way to get to the nearest village or town if you are lost. Most drivers would expect to get paid a tip if stopped for a ride.
Marshrutka minibuses can be found almost everywhere in Ukraine running through villages between larger towns, which is a thing next to hitchhiking and still very inexpensive.