-Allen key or wrench
-general purpose grease
Determine which size Allen key or wrench fits the pedal. Pedals can have a spot for an Allen key on the backside of the axle or they can have a flat spot for a wrench on the axle between the body of the pedal and the crank arm. Sometimes a pedal can even have both. Go for the larger, heftier interface so there is less chance of stripping the pedal or the tool you are using.
Find a nice flat wall to prop your bike against. It is always best to have your bike contacting the wall in at least 2 places, I usually have it touching in 3 places. The saddle, the back tire, and the end of the handlebar. That way it is more stable.
Position your crank arm so that the pedal is at the bottom of the stroke. Place the tool on the spindle of the pedal so that it is mostly perpendicular to the angle of the crank.
*Remember each pedal side has different threading. An easy way to remember which direction will loosen a pedal - when you try to loosen the pedal the cranks will want to spin (freewheel) on you.
This is the most dangerous part requiring co-ordination.
-Grab your rear brake so the bike doesn’t move
-Step on the pedal with one foot
-Place the other foot on the tool
-Push down with both feet to crack the pedal loose
A view of what my feet are doing
A view from the top. Remember to hold the brake so the bike doesn't move.
Now that the pedal has been broken free you can spin it the rest of the way out.
Clean up the threads and dab on some grease for re-installation
Clean up the threads on the crank
Carefully thread the pedal back into the crank making sure not to cross thread. Since tightening the pedal will try to move the back wheel just squeeze the back brake while you tighten it down to about an 8 out of 10 on the perceived exertion scale.
If you can't remove a pedal this way then your next step is a drill press ;-)