Taking off your "crank" and removing the crank spindle (axle) requires you to have two special tools: a crank puller tool and a spindle disassembly tool.  The crank puller tool allows you to apply reverse installation pulling pressure on the crank, in order to remove the crank off of the spindle.  When the crank is installed, it is literally pressed onto the spindle and the only way to remove it is to apply pulling removal pressure, in the opposite direction.  The second tool has special teeth on it to mesh with the spindle axle mechanism allowing tightening or removal of the spindle axle and it's bearings.  

The crank puller tool has two sets of threads: one on the outside to screw into the crank and one set of threads on the inside to allow the handle to screw in against the spindle and cause the reverse pressure necessary to remove the crank from the spindle.  The other tool has two sets of sprockets that mate with up to two different sized spindles nuts.  Only one set is used, the one that mates with the specific spindle nut on your specific bike. The outside nut is for application of a wrench in order to rotate the tool to remove the spindle nut.

For starters, first remove the bolt or nut or whatever, that is holding your crank onto the crank spindle.  On my bike, a normal 10mm hex key mates with the bolt.  A little ccw pressure, will remove the bolt attaching the crank to the spindle.  Since this bolt presses the crank onto the spindle, once this bolt is removed the special crank puller tool needs to be used in order to actually remove the crank from the crank spindle.

The outside part of the crank tool is screwed into the crank as shown below, with the handle portion nearly removed from the tool.  Hint; this tool has to pull on the crank so the threads of the crank puller tool have to be sufficiently deep inside the crank, to prevent the tool from stripping the threads, in the next step.

Once the tool is in positioned as shown, the handle of the tool is rotated CW until it meets resistance with the spindle.  Then you continue applying CW rotation until the crank is forced off of the crank spindle.  The crank (and chain ring if on the right side) should now literally fall off into your hands with the tool still attached. Remove the crank puller tool from the crank.  Do the same to the other remaining crank as necessary.  After the second crank is removed, the crank puller tool is no longer needed and you can return it to your tool box.

You can see how the spindle nut removal tool is applied.  Refer to this page for further instruction on how to remove and service the bottom bracket/spindle.

Now you can put the cranks back on.  Just slip the pedal cranks over their respective spindle knob and tighten down with a very healthy exertion on the tool tightening the bolt.  It is difficult to over tighten these crank bolts but it is real easy to not tighten them enough.  More is better.   Oh yeh, the crank with the chain sprocket, goes on the right side of the bike and the opposite crank should be mounted 180 degrees offset from the crank you are looking at. ;=)