Tip #1: avoid questions that are too general. Like this one. Your question is impossible to answer, but here are my thoughts anyway.

1. If this is a simple itinerary, you don't need award booking services. Go to a corresponding website and see what you can find. Be flexible. Always check one-way redemptions first and see where it takes you. That applies even to Delta that does not allow 1-way redemption for half the miles. BTW, when it comes to Delta do not get discouraged when you can't find anything at first; their calendar is broken.

Did I mention that you must be flexible?

2. Use the airline rules (especially stopover and open jaw) to your advantage. Learn the tricks. For example, never book US-Europe-US, instead book: Departure (NA, Mexico or Carribean) - US (real deaprture) - Europe - US (real destination) - Destination (NA, Mexico or Carribean). You can book 3 RTs with 2 awards if you're doing it right.

3. Getting direct award flights can be difficult or outright impossible. If you live near a small airport it will drive you nuts. Learn to be creative and book flights from major hubs. To get to those hubs use budget airlines, Amtrak or drive. Sometimes, it ain't 100% free.

3a. To get to a major hub, check budget carriers, such as Southwest, Frontier, and Jet Blue. Southwest and Frontier currently have excellent credit card sign up bonuses.

4. Do your homework and don't be afraid to ask specific questions in the right forum. Don't mind "snappers" either; some people won't feel content unless they put somebody else down.

Good luck!