In reply to wilkesley:
It partially depends on how adventurous you want to be. Do you want to have everything arranged before you set off or are you happy to make arrangements on the spot? Are you happy to do a standard trek or do you want to get off the beaten track (keeping in mind that even the most popular treks are still pretty quiet)?
Personally, I like CBT (www.cbtkyrgyzstan.kg) as they are committed to sustainable tourism principles and try to ensure that most of the financial benefits go to the local population rather than to Bishkek or abroad. I don't have any experience with their treks though, as I have only organised accommodation through them. However, in Karakol there are at least half a dozen tour operators, all of whom will be able to organise trekking trips. Again, the more standardised your trip is, the easier to arrange it while you're there.
If you want to be more organised or do a trip that is tailored for you then you'll probably want to organise something with one of the larger tour operators before you go.
Finally, I'd recommend spending a few days on the south shore of Lake Issyk Kul. It's fairly quiet, there are several places where you can stay in yurts on/near the beach and it's a nice place to recover after a long trek.