Ok, imma typin this from memory, so if I screw up anywhere, fill in for me, ok ?
Normally I don't remove the chain except to switch it over when doin this, but it's up to you.
Firstoff - remove the left pedal, don't ask why, just do it.
Now find a hex-key that fits the damn transmission-casing screws, should be 4-5mm, and there should be about 5 or 6 screws on the left hand side...make sure to remove only the ones holding that cover on, unless you like sitting in a puddle of transmission fluid.
Now...go get a big adjustable wrench, a flat edge screwdriver, an unsharpened #2 pencil, a rubber mallet, and a broom.
I know it sounds a mite ridiculous, but it works.
Jam the rear wheel with the broom, just stick it through the mags so the wheel will not turn real far...
Now, there's a large nut holding the sprocket on, but to get to it, you hafta deal with this little plate that's bent up at one side of it....you stick the screwdriver in there, assisted if need be by a little rubber-mallet action, and get it to where you can use the pencil and the mallet to flatten it out of the way so you can get the wrench on it.
Once you've done that, and put the wrench on it, figure out which it goes...I think it might be reverse-threaded, so you might have to turn it to the right to loosen it...make sure of that first, however.
(and this is why you jam the back wheel with a broom, see?)
Anyhow, between a little gorilla-arming and some more rubber-mallet frenzy, you should be able to get that nut loose...spin it all the way off and slip it over the left pedal arm.
Now gently pull that plate off, try not to mess it up or bend it too bad cause it hasta go back on there....slip that over the pedal arm too.
Now you just do the same thing with the sprocket, it should come right off but if it don't a couple light taps of screwdriver/mallet oughta do for it.
Now just slip the new sprocket over the pedalarm and push it into place....should have little "teeth" that mesh with where it goes.
Slip the plate back on, and make sure the little tab goes into the little hole in the sprocket, you will see what I mean when you have it in hand.
Put the nut back on, and tighten it down real good, cause it's pretty important that it not come loose, heh.
Now, the tough part, bending that plate back so that part of it rests against the side of the nut, it's doable, just have some patience and work on it with the mallet and screwdriver.....the plate keeps the nut from workin loose, you see.
Now, just slap the side cover back on and tighten it.
And then, put your pedal back on - Viola ! yer done.
Easy as pie.
Rear Sprocket info is gonna have to come from someone who's got the moped handy to look at, it's been a while since I've done that and don't trust my memory on it.
Although it should just be a matter of the rear wheel bolts (17mm) and then whatever holds the rear sprocket on.