One method of tapping a hole is with a drill. This method requires a little more finesse than tapping with a hand tap but can be used to tap all types of metals, including stainless steel.
Use a high grade cutting fluid such as the kind pictured above and re-lubricate the tap for every hole
Use a good quality tap (not the kind found at Canadian Tire). A tap such as this one 10-32 HSS 2 Flute H3 works well.
Ensure that the tap is well secured in the drill.
Do not use pressure; let the tap pull itself into the hole.
Use a drill with variable speeds (like most battery powered drills) not a drill which only has an ON/OFF setting such as drill presses and most corded drills.
Hold the drill straight at a 90 degree angle to the work piece. Any lateral movement will snap the tap and/or result in an improperly tapped hole.
When you feel it binding or hear it squeaking stop the drill, reverse and back off the tap, then tap again.
Make sure the piece being worked on is well secured in the vice.