I have exactly zero experience with arduino but I am completely intrigued by it and want to jump in.
To start, I need to learn how to use arduino to power a 7 volt drill for six seconds, then reverse polarity and run it for another six seconds, then turn off.
Arduino does not have 7 volts available for controlling the motor in the drill, and most important Arduino can not supply the current to drive the drill.
But with an external powersupply to power the drill and a thing called an H bridge (basically an IC) you can control the drill from Arduino.
Search the forum for H bridge or google arduino + H bridge.
The last piece of information you need to find out is what is the worst case load current the drill will draw under real operating conditions?
H-drives are sold by the max voltage and current capacity they can work with. So you need a digital multimeter set up to read DC amps and then use your drill with the mechanical load you need turning and measure the current. Whatever it is the H-drive you select should have a rating of about double that for a good safety and heating margin.
So you need a digital multimeter set up to read DC amps and then use your drill with the mechanical load you need turning and measure the current.
This assumes that the motor won't exceed the max current rating of the meter (which for most small meters is around 10 amps); if it does, then "poof" goes the meter (well, the fuse inside, likely).
If you think the motor will pull more amps than your meter (or you know it does because your meter now no longer measures current!), then measuring the voltage drop across an appropriate sized shunt (essentially a very small value, but high wattage resistor - there do exist purpose-built shunts, but a 10-15 watt 1-ohm resistor would work OK - you can also build a shunt using solid copper wire of an appropriate gauge; knowing the gauge you can find out the resistance per foot and thickness, then build a shunt based on that info - plenty of places and videos on the net available - just look up "homemade shunt") would be the next step.