Ukrainian is an official language of Ukraine. However, Russian is widely in use in the country. Most people in Kiev and in Eastern Ukraine speak Russian as a main language, while Ukrainian is a main language in Western Ukraine. If you are familiar with one of these languages you will be able to communicate with Ukrainians without any problems.
It is interesting, and quite evident, that in rural areas Ukrainian is spoken more than in big cities, which represent a bilingual society of the country. Very often one can even hear the mixture of the two languages, Russian and Ukrainian. The situation when one interlocutor speaks, for instance, Russian and another one - Ukrainian is possible even on TV or over the air.
As of English, now more and more people learn this language, which is the most popular one among other foreign languages in Ukraine. Major restaurants, bars and hotels have English speaking staff, but in general not much English is spoken in Ukraine. We recommend that you have a phrase book at hand or someone who can help you (at least for your first day in the country).