Bottom, 4 inch square steel bench block, wood block, a small jar of liquid bur-life (I pour in about an eight inch depth, and use this to dip the end of the drill bit to lubricate it, and then drill),  Xuron flush cutters. roll of 16 gauge wire.

Gauging the correct length of wire can be tricky.  I use gauges made from brass sheet, as follows:

For an 18 gauge wire rivet, I punch a 1/4 inch hole in two pieces of 24 gauge brass sheet.  You need two gauges to measure the end to end length of the rivet.  The drill size for the rivet is a No. 60.

For a 16 gauge wire rivet, I punch a 1/4 inch hole in two pieces of 22 gauge brass sheet.  Drill size for the rivet is a No. 55.

For a 14 gauge wire rivet, I punch 1/4 inch hole in two pieces of 20 gauge brass sheet. The drill size for the rivet is a No.52.

It doesn't have to be a 1/4 inch hole.  This was the size already set-up in my punch.

If the metal distorts, whack it with a soft face hammer. I use my "go to" hammer for this.  For accuracy, it's important to keep the metal flat.

The gauge example shown in the photo, shows the hole close to a corner of the sheet.  After placing a rivet or two, depending on the size of the piece, you may find the other rivets, or parts of the elements, getting in the way of your gauge.  Placing the hole near the corner of the gauge helps avoid this.

It is always a good idea to check your wire because there can be a slight difference in the diameter of the wire.  Drill a right size hole in a piece of scrap metal and test the fit. Adjust accordingly. Having a full set of number drills is handy.  You can always use the larger sizes to make decorative holes in an element.

Procedure:

1.  Clamp the two parts of the piece tightly together.  This is where the Speetog Plier/Clamp comes in handy.  A ring clamp, or parallel jaw pliers can be substituted.

2.  Center punch where the hole for the rivet is to be placed.

3.  Place the element over a wood block and drill the hole with the appropriate size drill bit.  14 gauge wire, No.52, 16 gauge wire, No. 55, 18 gauge wire, No. 60.  It is important to drill straight, avoid wobbling. I did not include 20 gauge wire as it can be more difficult to rivet.  Drilling two or three pieces together at the same time will ensure the hole is accurate through all the pieces.  I much prefer to use a drill press.  That  insures a straight hole and a much steadier feed rate of the drill into the metal.

4.  Dress the hole with a setting bur, front and back, putting a little chamfer around the hole.  Brush away debris.  A larger size drill bit can also be used.

5. Using flush cutters, cut a off short length of wire, an inch or less.  Short wire length works best for me.  Many so-called flush cutters leave a tiny "pip" on the end of the wire. Square up one end of the wire with a file.  Filing may leave a tiny bur on the edge which could make it difficult to get into the hole.  Gently file round the end of the wire.

For the next steps, keep everything snug on the bench block.

6.  Lay one of the gauges on steel bench block, hold the still clamped pieces to be riveted on top of the gauge, hole over hole.

7.  Holding the wire in a pair of pliers, insert the filed end into the rivet hole.  Make sure it goes all the way through and hits the bench block.

8.  Insert the second gauge over the wire.

9.  Lay the flush cutters flat against the top of second gauge, making sure all pieces are flat against one another, and cut the wire.  Leave the gauge in place.

10.  Carefully file the end of the wire removing any burs. Leaving the gauge in place will insure that you'll file just enough. Sometimes, you may find your wire cutter leaving more length than necessary.  File the wire end until it even with the gauge.

11.  Remove the top gauge and form the top of the rivet.

12. Turn the piece over, remove the bottom gauge, and finish forming bottom of rivet.

That is one way to do wire rivets.