I'm currently in Krakow and am planning on going to Lviv next. Rome2Rio indicates that this is a 6-10 hour land journey either by bus(es) or by train(s).
I've heard from another backpackers in my hostel that you can't take the train directly because there's a difference in rail gauges, so you have to do a train switch on the Polish border in the town of Przemysl.
Other than this, are there any other intricacies involved in crossing the border? I was considering doing a night bus/train given the length of the journey, but if border control is a hassle I might rethink that plan.
I've a US passport and am intending to enter without a visa since I don't plan to stay 90 days. The US State Department page on the Ukraine indicates that I'll need proof of health insurance and adequate funds, both of which I have.
(I'm generally not familiar with crossing land borders other than Vietnam-Cambodia, US-Canada, Malaysia-Indonesia, and within the EU.)