You can travel to Ukraine by bus or train. Information on travelling by train can be found here.
Flixbus
There are buses running to Kyiv and Lviv. You will have to change once. The journey costs up to €160. Journeys for the next few days are generally fully booked.
The timetable and prices can be found online at global.flixbus.com.
Benz Express
On Tuesdays, Thursdays and Saturdays, a Benz Express bus travels from Leipzig to Ukraine. The journey costs € 80-90.
The timetable and prices can be found online https://busreisen.com.ua/.
ODRI
ODRI travels regularly to Ukraine. The timetable and prices can be found online www.odri-ua.com.