I like studying Buddhism, especially Prasangika, but I find I sometimes get kind of conceptual. I practice shamata every day, but if a beginner like myself wants to try meditation/mindfulness with koans, where should he begin? Any general tips for dos and don'ts?
At the behest of ChrisW - not to sound flippant, but you really do need a teacher if you are going to study koans. At their very core, koans are asking you to look at something outside your current way of seeing the world. Unfortunately, you simply can't use your current system of thinking to correctly discern something outside of it. (Godel, Escher, and Bach, right?) You absolutely need a second opinion - someone with confirmed understanding - and that's where a teacher comes in.
By going at this yourself you run the risk of falling into two traps. On the one hand, you might come to mistakenly think you've understood something. We are great at deluding ourselves, after all. This is especially true when it comes to our habits, preconceived notions, and obstacles (you know, the very things koans seek to rout out!). Without a teacher to point out that your understanding is less than ideal (or entirely wrong!) there is no limit to how screwed up you can get.
On the other hand, and this happens with quite a bit of frequency, sometimes we actually see the very thing a koan is pointing at, but ignore it or don't take it to be significant. Seeing into a koan isn't exactly accompanied by the singing of angels. Well, sometimes it is. More often than not, however, you aren't even going to understand what it is you've seen. At the very least, you aren't going to understand why it's important. I once sat with a koan for years thinking I hadn't answered it when I had actually seen into the very first week. Me, in my boundless stupidity, just assumed that I was supposed to be looking for something more significant than what I was experiencing! If I didn't have a teacher (who finally demanded a black and white, literal report on what was happening with my practice) I might still be sitting with that same koan today!