Getting to Lviv by bus can be either quite comfortable and relatively cheap - if you take a long-distance one (at least overnight) or a pain in... (try it and choose a word) - if you take a bus from any town in Eastern Poland...
     As for trains - Lviv is a regional railway cross-point and should you travel to any place in Western Ukraine or from/to Ukraine western neighbour countries, you'll probably go through it. There are trains to Berlin, Wroclaw, Warsaw, Prague, Viena, Budapest, Belgrad, Sofia, Venice and to several places in former USSR. It's a great point to start a train-trip through Ukraine and to get acquainted with a unique soviet railway system. Trains in Ukraine are quite slow, but these coming from Western and Middle Europe to Lviv are even slower - due to changing the rail gauge. Many railway fans are traveling to Ukraine by train just to see the rail exchange operation...