Anytime I travel I check the room like a hawk before I take any of my things in.
As a few people have posted already: pull off the sheets & look in the seam of the mattress. Check the headboard & night stand. You are not necessarily looking for the bug themselves as they are usually dormant during the day. You are looking for their (so gross) feces. Tiny black spots. You can google search bed bugs & see detailed pictures on what to look for.
I also (just for peace of mind) always ask the hotel manager what they do to prevent the spread of bedbugs in their hotel.
Another place I check..... Go to expedia.com & pretend like you're wanting to book that hotel. Go to that hotel's page & read the other guests reviews. I dodged a hotel infested by bed bugs because of that. And it was a big name hotel.
Good luck & have a good vacation. :)