Good answers already.
Let me just add two tips:
First, recognize that it is a partnership--you and your Realtor. While you definitely should have a Realtor set up a search, I'd encourage you to regularly review the MLS as well. It's possible, for instance, that the parameters your Realtor might set up might be a bit narrow. You might spot a property that you'd be interested in that doesn't meet 100% of the requirements you specified to your Realtor. In that case, bring that specific property to the Realtor's attention (so that perhaps you can look at it) and so that the search parameters can be modified if appropriate.
Second, sometimes agents do have access to listings you wouldn't. Our office has a weekly sales meeting. One part of it involves going around the room with agents announcing upcoming listings. For instance: "I'm going to have a listing next week in Colchester Hunt--a really nice 4 bedroom, 2.5 bath house. The kitchen's been redone and it's got a great back yard. We'll be pricing it around $525,000." Now, that house isn't on the market yet, so it's not on the MLS. But one of the other agents at the meeting may have a client looking for a 4 bedroom in the $500,000 price range. Pretty frequently, a buyer's agent will approach the listing agent and say, "I have a client who I think would be interested." So, you might see that house come on the market and then go under contract the same day. The client with agent got a 2-week head start, and snagged the home before most buyers scanning the MLS would have even seen it.
Hope that helps.