If you're used to the Latin Mass, you know what to expect, more or less. Except it's much more antique than the TLM and, if you go see the Melkites or the Ukrainian Catholics, don't be too surprised if there are no pews. Also, don't hesitate to ask the priest things after the Divine Liturgy ends, Eastern Catholics tend to have their own perspective rather than just being cooky Roman Catholics with icons.
It would be neat if you came back to tell us your experience as well.