This will cover setting an eyelet without the special eyelet pliers, a bench mounted press, or a hydraulic press. You will need a hole punch, the eyelet tool (or tapered punch large enough to spread the eyelet) and an anvil of some sort with a hole.
Step 1: Punch the Hole.
Using either a leather/ fabric hole punch tool, a round tubular hole punch (often included in eyelet kits), or as a worst case a pair of scissors (be careful not to make the whole too big here), punch a hole the size of the center portion of your eyelet.
You can use scissors if you have no other hole punch, I usually cut an x on the center of my hole then remove the excess material if I do it this way.
Step 2: Assemble Eyelet Parts in Hole
Now that your hole is punched, put the male end of the eyelet through the hole. You want the male end on the side that will be most visible as this side is the better looking. Once the male end is through the hole, place the female end, or washer over the post.
Step 3: Spread Eyelet and Set.
With the two ends of the eyelet assembled around your material, you can commence to setting the eyelet. Using your eyelet tool (or tapered punch) and your anvil, place the eyelet in the anvil with the post facing up and the female end (washer) towards you. Place the tapered end of the eyelet tool into the post and hammer. I find that two or three solid hits from a metal hammer, or a few extra from a wooden mallet usually do the trick.
Check to make sure that all the excess material has been spread and the eyelet is snug, and you are good to go.