I want to make a mortise and tenon joint that will be held together with a dowel instead of glue. How can I drill the hole in the mortised stock and the tenon so that they line up accurately and produce a tight joint?
The point of the dowelled/drawbored mortise-tenon joint is not to line up the to parts, but to create a tension that draws the tenon tightly into the mortise.
Therefore, rather than drilling though the mortise and tenon together, the drilling process is divided into three steps:
Offsetting the hole in the tenon, towards the mouth of the mortise, will draw the tenon into the mortise, creating a tight fit that does not require glue if cut precisely.
Because of the "re-use" of the drilling configuration in step 2 and 3, a drill press is preferable to hand-held options.
The corresponding technique for a through mortise-tenon joint would be to add a wedge trough the tenon on the outside of the joint - with the added benefit that the joint can be disassembled and resembled later, where reassembly of the drawbore mortise-tenon might loosen the fit, to the point where the dowel has no real effect.
I've added this answer because I feel ChrisF's answer is inaccurate, and kwakmunkee's relies on an external source that might disappear.
ChrisF's solution will provide you with nice, stable drilling support and it will make sure the holes line up perfectly on both parts. But if you don't want to use glue, keep in mind that it's not necessarily a bad thing if the holes don't line up perfectly; in fact, there is a specific technique called "drawboring" that requires this and makes an extra-strong joint.
Basically you drill the hole slightly off-center in the tenon and then chamfer the inside end of your dowel. This makes the mortise pull the tenon in mechanically as you pound in the dowel. The technique is the subject of a recent Wood Whisperer video: http://www.thewoodwhisperer.com/videos/drawbored-mortise-tenon/
The simplest solution is to drill the dowel hole after you fit the joint together.
Fit the joint and make sure everything's square and true, then drill straight through the mortice and tenon in one go and insert the dowel. Chisel/plane and sand it flush and you should be good to go.
Making a mark on the outside of the mortice where you want to drill will ensure you get the location right.