Hi! There are buses and trains you can use to get to Donetsk from Kharkiv and vice versa. You can buy tickets for trains here:
1) Brand new online-ticket-store at official Ukrainian Railways website:
http://booking.uz.gov.ua/en/
(notice that there is a small bug there giving you time according to the GMT in you computer. The real local Ukrainian time is 05:55 - 12:45)
2) www.e-kvytok.org.ua
If not working at the moment, try http://www.e-kvytok.ua (although only in Ukrainian).
3) Otherwise you can try some private commercial ticketresalers.
For example:
http://gd.tickets.ua/en OR http://dprc.gov.ua/index.php?set_language=1
By the way, check this book Travel Ukraine: Kyiv, Kharkiv, Lviv, Donetsk. there are a lot of useful information about Ukraine and each city in particular. Yo uwill find info about railways, bus stations, taxi services, food, attractions and tips how to survive i nthis country. It is a must have for tourists.
Edited by: emd_two on Mar 28, 2013 2:30 AM