Shop early and shop often. Your chances of getting what you want are best the earlier you try - especially if your dates are not flexible.
You really need to know what you're doing in order to make this work. This website is great for tips on European travel, but it's not the authoritative source for inside info on how to win at the very complicated frequent flyer game. Google "FlyerTalk" and prepare to spend some time getting a valuable education there.
I just (2 hours ago) booked award travel for me and the wife this fall from Seattle to Thailand, with a stopover there for a few days, then on to our destination in Indonesia, then return about 3 weeks later. It's a long, convoluted route (Seattle, Tokyo, Bangkok, Bangkok, Singapore and Jakarta; return Jakarta, Singapore, Seoul, San Francisco, Seattle).
Buying this ticket would have cost us big bucks, but we paid just $110 total plus miles (just 65000 miles each - you can almost get that for signing up for one credit card). Quite a deal. But you have to know the sneaky rules of the game.
Now I just need to scavenge a few more miles for a couple tickets to Greece the following spring... I loves me the frequent flyer tickets. :)