Case matching should be pretty self explanatory -- put your new base gasket on the cases, (make sure it matches the cylinder first), mark where it is, and then cut away the places that are marked. You just want the transfers in the case to match the transfers on the intake because that makes everything flow better.
Matching ports is different from changing port timings. If you mess with the shape of the ports in the bore (where the piston is) rather than just messing with the outsides of them (like by case matching or matching your exhaust port to a new pipe), you can change your port timing. When your ports open and close, (aka where in the rotation of the crankshaft the ports open and close), how long they are open or closed, and how the ports are shaped are all vitally important to making your moped perform a certain way. When you change a port's timing, you are modifying the port on the inside of the cylinder so that the piston will open or close that hole at a different time, or so that the mixture will flow differently through it.
For example, in the image below, the top "engine" shows a representation of how a stock cylinder might be. The bottom one shows how someone might modify their exhaust port. In both images, the piston/crankshaft are at the same point in their rotation. Let's just say that it's at TDC in both images. However, as the piston starts moving back towards BDC, it will begin to uncover the top edge of the exhaust port on the bottom one before it would start to uncover the top edge of the exhaust port on the bottom one. Within bounds (and I really shouldn't generalize like this, but...), having the exhaust port open sooner will help the exhaust gases escape better and more completely (and probably some other stuff that I am not enlightened enough to know), which can help performance. However, if you have it open too soon, then too much of the fresh mixture coming in your intake can go out your exhaust, which can decrease performance. There are similar rules and tradeoffs for changing the intake, transfer, and boost ports, although I'm really not even qualified to be explaining it this far, so I should stop now before I butcher it further. Long story short, if you don't understand how certain performance characteristics will change when you change the port shapes or port timings, then you probably shouldn't change them. Port matching is pretty safe, though, and if you really want to change the insides of the ports, then widening the ports (up to a certain % of the bore) is relatively safe. If you want to read up, check out the links to Jennings and Bell on the performance tuning page on the wiki.
And yeah, I know you asked for a video and not a 5-paragraph essay. I guess I'm just not sure how a video would help, unless someone spent a lot of time and effort explaining what was going on. Seems to me like doing it is the easy part, and knowing what to do and why you do it is the hard part.
As always, someone correct me if I'm wrong....