Tatra mountains span across border between Poland and Solvakia, so most people you may meet there will speak in languages of these countries, but communicative english is also very common. Staff at mountain refuges should be able to communicate in english too.
Most interesting part of these mountains is under national park protection, so if you want to see it, you will have to walk a lot. Mountain range has many trails for both experienced and novice hikers, so navigation is not a problem, but checking difficulty of trail before setting of is mandatory if you want to avoid unpleasant suprises. Another thing worth noticing is that some harder trails are one-way only, and can be pretty dangerous under bad weather conditions.
On Polish side it is the best way to get around outside national park, because buses are cheap (3zł ~ €0.7), arrive and depart very often, and sometimes it is possible to negotiate the route.
There is railway parallel to mountain range in Slovakia, so in addition to being convenient mean of transport it provides astonishing views on High Tatras. In the winter it is also good for getting from one ski resort to another.