The next step is to make the rivets. Wedge rivets are made by flattening a piece of wire, and then using an end nipper to cut small triangles (wedges) from it:
Once you have rivets, the next step is to set them in the rings, thus riveting them. This can be done by hand, with nothing more than a hammer. However I have found it convienent (and quite plausible) to construct riveting tongs. NOTE: details on constructing these tools can be found in the Riveted Maille Index.
To use the tongs, first get a ring and a rivet ready:
Then set the rivet in the rivet hole:
Then position the pointy end of the rivet over the deep pocket in the rivet tongs. Squeeze the tongs to drive the rivet into place:
Now that the rivet is set, the pointy end must be peened. Move the pointy end of the rivet into the shallow pocket of the rivet tongs, and squeeze the tongs again, thus peening the rivet and finishing the ring: