Step 1: What you need
A small reel of enamelled copper wire.
A drill bit of the desired internal diameter of the coil.
Soldering kit and solder.
Wire snips and needle nosed pliers.
For Niftymitter, use 0.75mm (or 22SWG) diameter wire, such as this from Rapid and a 5mm drill bit.
Step 2: Turning the wire
Using the drill bit as a template, wrap the wire, counting up to the number of desired turns. Allow 3cm of wire clear before starting the turns and keep the wire taught while turning. Kogawa has a video for this step on his site here [.wmv].
For Niftymitter, make 4 complete turns, as close together as possible.
When complete, snip off from the reel at 3cm distance from the last turn.
Step 3: Forming the legs
Step 4: Tinning the legs
The legs of the coil require tinning to remove the enamel and prime the surface for soldering onto a board.
Use some needle nosed pliers to grip the coil while tinning - it can get very hot. Heat one leg with the soldering iron for a few seconds.
Introduce some solder to the heated leg and continue applying the iron, moving back and forth on the leg. The enamel will begin to separate from the copper and bobble.
Repeat the procedure for the other leg. When complete, snip of the ends of the legs, with the surplus solder attached, leaving at least 1cm of straight leg before the turns.