Kharkov is a city of nearly two million people and is located to the east of the Ukrainian capital city Kiev, not too far from the border with Russia. It is best known in Eastern Europe for its many educational establishments and in particular it's universities.
The city attracts students from all over Europe, the middle east and even as far afield as China. High quality of teaching and at a very low cost when compared to western European prices. Kharkov is also a host city for the Euro 2012 football competition, the local football stadium which is home to the team "Kharkov Metallist" is one of the confirmed venues along with others in Ukraine and Poland.
To get to Kharkov usually means flying into Kiev and then making an onward journey heading east. It is possible to book one of the frequently departing domestic flights to Kharkov but there are other options:
If you were with a group of friends trying to get to a football game in Kharkov then hiring a car from Kiev and taking a seven hour drive east is certainly an option, it may even be quite fun as Ukraine is a truly unique country. However there are some practical issues you need to first be aware of:
1) The police in Ukraine regularly pull over drivers and extort them for cash, they may target hire vehicles and this is even more likely during the football competition when the country is full of wealthy western football fans.
2) The roads in Ukraine are in very poor condition, especially outside of the capital city Kiev. Think pot holes that will easily shred car tyres.
3) Street lighting is kept to a minimum and there is a general lack of road signs outside of the cities.
A much safer option, but you do need to make your way to the central station in Kiev as there is no station at the airport. You can use a taxi, bus or the popular Marshructka (share taxi) as a way of getting to the train station.
Trains depart five times per day with an additional night service. You will most likely need to book your ticket in advance. If you just turn up at the station then you may not get a seat.
You can book a coach ticket, the vehicle departs from outside terminal B at Kiev Borypil Airport and makes several stops before reaching Kharkov central bus station. There are several departures throughout the day and one night service. The cost is affordable but the roads between Kiev and Kharkov are so bad that it will not be the most comfortable journey you have ever undertaken.