I've had a lot of questions about how to guide small taps from members of our club so I took this picture to show some of the tools I use.
The small one on the left is dedicated to 0-80 taps, held in place with a set screw bearing on one of the tap shank flats. As with all the tools shown, the 1/8" freewheeling rod on the top is grasped in the drill chuck after drilling the properly sized hole. The 1/2" diameter fluted portion is turned with the fingertips. Very sensitive and difficult (though not impossible) to apply enough torque to break the tap.
Next to it is a similar model for slightly larger taps (e.g. #1,2). The removable black torque enhancer screws are almost never used since the knurled portion allows for sufficient tapping torque. Rather than simply drill a hole the size of the tap shank, I fitted this one to take "collets". The example lying in front of this tool is a collet to fit 00-90 taps I have. These collets are nothing more than 3/16" stock, drilled through to accept the tap shank. For half the length of the collet, half of the diameter is cut away. This exposes the tap shank so the setscrew in the tool can grip it.
Next is a slightly larger version for taps in the #3,4,5,6 range. The permanently mounted torque handles provide enough torque for any tap that will fit into the tool.
Finally, on the right is a low profile (I have a mill/drill with a round column) tool that, using collets like the one shown, can handle the larger taps.