Welcome back, class!  Now that you've adjusted your Shimano Nexus hubs, we'll dive into the next most interesting operation on one of these bikes: rear wheel removal.  Mastering this will allow you to replace tires or tubes that are worn out or damaged beyond patching.  This will get a little more technical than the previous post, so it's very important to make sure you're comfortable using tools and that you have the time and energy to safely put everything back together.  Please read through the entire post before tearing apart your bike, and be sure you're comfortable performing all the operations described (especially tensioning the chain!).  Troubleshooting and adjusting your hub didn't require any tools, but this will, so get out that toolkit and polish up your:

1. 15mm open-end wrench or 15mm deep socket w/ driver
2. 10mm open-end wrench and 10mm socket w/ driver (you can substitute another 10mm wrench or a small adjustable if necessary)
3. Cable cutters (diagonal cutters or wire cutters can be substituted)
4. 2mm hex key/Allen wrench
5. Dental pick, sharpened spoke, sturdy ballpoint pen, small switchblade, or something else with a nice point to it
6. Tire levers (if you plan on replacing tubes or tires)

Now that your tools are prepared, set your bike on its center stand (or clamp the seatpost in a work stand if you're lucky enough to have one).

We will remove the rear wheel first because it's a more complex operation and many of the steps will be duplicated in removing the front.  As an overview, we're going to disconnect the brake, open the chain case, disconnect the shifter, disengage the chain tensioners, and remove the wheel.  Then we will reinstall the wheel, engage the tensioners, tension the chain and center the wheel, reconnect the shifter and brake, and close the chain case.

To disconnect the brake, first loosen the cable fixing nut several turns.  Pull or clip off the cable tip, and pull the cable out of the brake.

Now once we've removed the torque arm clamp bolt the brake will be completely disconnected.

After that, move back to the right side of the bike and open the chain case, starting by unhooking the tension wire running along the bottom of the case.

Once the wire is unhooked about 3/4 of the way down toward the front, unsnap and unclip the rear section as we did in the previous post.

Now loosen the axle nuts about three turns (Don't worry, the chain tensioners will hold the wheel in place) and yank the rear section of the chain case frame straight back and out of the bike.

Shift the bike into first gear, and poke the long end of the 2mm hex key into the tiny hole in the back of the cassette joint.

Pull downward on the wrench to give yourself some cable slack, and then use your pointy tool to pop the cable and cable stop out of the cassette joint.

Pull the cable housing out of the housing stop, being careful not to kink the cable.

Now that you've disconnected the brake and shifter cables from the hub, all that's left is removing the wheel itself!  Loosen the chain tensioners until the nuts are even with the end of the threaded section, and loosen the axle nuts until the colored non-turn washers (yellow on the right, brown on the left) can completely clear the frame.

Lift the chain carefully off the teeth of the cog and set it down on the plastic of the cassette joint.

Now you'll actually remove the wheel: pull it straight backward until both chain tensioners are loose enough that you can flip them downward so that they hang from the axle.

The wheel will now be free to slide forward and out of the dropouts, and you're free to replace tubes, change tires or just marvel at your accomplishment.

To reinstall the wheel, you will essentially be reversing most of the steps you've just completed.  Set the chain on the cassette joint -- next to the cog but not on it -- and then slide the wheel back into the dropouts.  This may take some wiggling, and possibly even some fiddling to make sure that the chain tensioners are inside the dropouts, and the non-turn washers (brown and yellow) are outside.  Gently pull the wheel as far back into the dropouts as possible, giving yourself enough slack to flip the tensioners back into place.  Now that the wheel is held in place by the tensioners, you'll be able to reattach the shifter and brake cables, the chain, and the chain case.

Set the chain back on the cog and carefully turn the cranks a few revolutions to make sure that the chain is fully set on the chainwheel (front gear) as well.  To reconnect the shifter cable to the cassette joint, first slide the cable housing end into the housing stop.

Now repeat the trick with the 2mm hex key to wind the cassette joint back to a point where you can slot the cable stop into its cradle, making sure that the cable sits cleanly along its channel.   Shift up and down the range a few times to make sure that everything is working smoothly, and also use this opportunity to check the adjustment of your hub (just like you learned to do in the last post!).

Pass the brake cable through the housing stop and into the cable stop, tightening it down at at its original setting.  Make sure the housing is fully inserted in the stop.  At this point you can crimp a cable end cap onto the cable, then test brake function by pulling hard on the brake lever. 

Slide the rear section of the chain case frame into place, carefully pushing both top and bottom ends into place in the main chain case frame.  Be sure that the chain tensioner is outside the chain case frame on the axle.

Now that everything on the axle is in place, you can tension the chain.  This step is going to be the most technical that you'll perform during the operation, so shake the kinks out of your hands and get ready!  Tighten down the axle nuts until the tabs of the non-turn washers are fully inserted into the dropouts, but not so tight that you can't shift the wheel.  Throughout this step, you'll be keeping the wheel centered in the frame by watching the distance between the (ideally fully inflated) tire and the chain stays.  Tighten the chain tensioner nuts evenly as you bring the wheel back toward its original position.  On Workcycles bikes (especially if you are using the original cog size), you'll frequently be able to find this spot by the indentations left by the non-turn washers in the frame powdercoat.

Ideal chain tension can be an art and a science, but the easiest gauge will be this: at the tightest spot in the rotation of the cranks (because there will be tight spots and loose spots) you should still be able to move the chain slightly (<1/4") up and down with your fingers.  You should NOT hear a crackling sound as you spin the pedals through the tight spots, and the chain should not be so loose as to hit the bottom of the chain case.

Once you've got the chain at a nice tension, double-check the centering of the wheel and then reattach the rear brake's torque-arm clamp on the chain stay.

Now you can tighten down the axle nuts!  Make sure these are solidly tight, really get your arm behind the wrench (unless you're some sort of giant burly guy, in which case you'll want to exercise some restraint).

Now that the wheel is reinstalled and the chain case frame is reassembled, most of what's left should be familiar from the last post: closing the chain case.  Gently (because these are fabric parts, after all...) slide the rear section of the cover over the frame, keeping the chain tensioner outside.  Pull the edges of the inside slit (between the wheel and the chain case) together and slide the prongs of the clip into their pockets inside the chain case.  Snap the snap on the outside, and hook the wire back and forth across the hooks on the underside (don't miss any!).

...And you're done.  Go for a ride!