Well, that's a big question. Our ship, The Enterprise, has been all over the galaxy, more planets and systems than I can count. Our mission is exploring, after all.
But it's a little easier to answer the other part. The first human craft achieved faster-than-light speed, or Warp Drive, on April 5, 2063. I'm from the 24th century, so it's been a few hundred years since we've been out there exploring the universe. [He could go on since through a quirk of time-space he was actually there, but there's a LOT happening at the moment with the Captain so he'll keep it brief.]
Anyway, I'm the Chief Engineer on my ship and Warp Drive is one of my specialties, so if you have any questions I'd be glad to try and answer them.