I'll give you a short how-to:
Whe you get the new kit, it will consist of a couple of parts:
Small-end "bolt" and sometimes a bearing
Sometimes a head
To properly install this, do as follows:
Mount the piston to the small-end with the bearing and close it with the 2 circlips. Have the arrow point down, to the exhaust port.
Now put a base gasket onto the cilinder.
Grease up the cilinder wall with a little bit of 2-stroke oil. Do the same for the piston. Get all the surface covered with a thin film of oil.
Put the piston ring(s) on the piston. Mind the little nodges in the piston, or the rings won't fit.
Compress the first piston ring between your thumb and index finder and slide the cilinder, on the mountingstuds, over the piston. If you have a second ring, do the same for that.
If the 2 rings are in the cilinder, you can now "mount" the cilinder by pressing it softly against the engine.
Apply some pressure to the top of the cilinder and turn your flywheel to see the deckheight. If it is too little, (IE. the piston gets higher than the cilinder wall) add another base gasket.
If all looks well you can put a head gasket on and mount the head.
Tighten the bolts crosswise. IE. If you number the bolts clockwise
Start with 1 and tighten till you feel just a hint of resistance and then go to 3, do the same, then 2 and then 4.
Then tighten em all the way in the same order.
Now don't get excited, you're not done yet!
Turn the flywheel slowly, by hand, to get atleast a few full strokes. Make sure the piston doesn't touch the head. If it does, add another base gasket. Never add another head gasket, this will mess up your compression and it'll soon start to leak.
If all is well, upjet if you come from a 50cc add a spark plug and then start the engine. After starting, let it idle for about 2 minutes and then turn it off.
1 last check: When then engine is warm after 2 minutes of idling, turn the flywheel by hand and see if it is still smooth. If it hits the head, again: Add another base gasket. (About 3 basegaskets is the maximum. There are special thick gaskets for sale.
That's it. You're done.
For breaking it in: Add some extra oil to your fuel (About 1:40) and take it easy for the first 20 minutes. No full throttle or high revs. After 20 minutes you can make more revs. Making high revs while breaking in is not bad. As long as the cilinder is nice and warm and you remember not to keep the same RPM for more then a minute.