The eyelets are a little brass or aluminium ring. The small ones are a little bit smaller than your fingernail of your little finger. They are usually available from haberdashers or stores that sell sewing/dressmaking equipment (threads, fabrics, etc) and you can buy a small kit that comes with a short steel rod. This rod is placed over the two-piece eyelet and then a few sharp taps with a hammer and you will have an eyelet.
You basically take the typewriter ribbon, cut a small hole in the centre of it, push one piece of the eyelet (usually, it's the longer section that looks like a top hat) through it and attache the other part, which looks like a ring, on top of it. Tap it with a hammer and the top-hat piece flattens and secures to the ring and bingo!, you have an eyelet on the end of the typewriter ribbon.
None of this makes any sense now that I read it, but once you get a packet of eyelets, it will be a lot clearer.

This video shows the basic principle behind what I just said. This is for tents. For typewriter ribbons, everything is much smaller, obviously. Forget the large hole cutter that's used in the video. For typewriter ribbons, you just have to make a cut that's large enough to fit the long eyelet piece through, rather than cutting a perfect circle through the ribbon.

https://www.youtube.com/watch?v=bA2WvPEY7M4

Best of luck, but it's easy once you practice a few of them.


 

Eyelets should be placed about six inches from each end of the ribbon. Some say you can tie a big knot in the ribbon at that point and it will work. I have not tried that. I always buy my generic ribbons with the eyelet, and then cut it off if the machine doesn't use it.