There are other methods for DIY ice tires (like sheet metal screws in mountain bike tires), but these ones made with pop rivets are elegant and suited to narrower tires used on hybrid/cross/touring bikes.
Step 1: What You Need
An awl, or sharp poking thing (not a drill or blade).
A knife if you want to slice off tread blocks (not pictured)
Some steel pop rivets, long enough to reach through the washer and tread. The ones I used were 1/8" capacity, for a pretty ordinary cross tire. If you have very deep tread or puncture resistance layers in your tire you might need longer ones. I wound up using 33 rivets in my rear tire and 90 in the front.
Washers just big enough to fit over the rivet body--some are usually sold alongside the rivets.
Some cyclocross tires (not pictured) -- I got some off the used rack at my local bike shop. You want tires with some good tread to propel you in snow -- the rivets will help with ice and strong hardpack..
Step 2: Pick a Pattern
The studs should be placed a little off center, so that they contact a hard surface when rolling, but you mostly roll on rubber. That way you keep traction on paved surfaces, but the rivets can bite in when you are on ice.
With a cyclocross tire with little knobs, it can work well to slice of some of the knobs in the pattern to be replaced with rivets.
Step 3: Set the Rivets
Then load up a rivet in the rivet tool and wriggle it through the hole from the inside of the tire -- again, you're trying to get it between the tire cords and not tear them. If this is too hard, try finding a bigger awl.
Finally, load a washer on the rivet body outside the tire and set the rivet. It leave a sharp-edged nub sticking up from the washer that is good at biting into ice.
Step 4: Enjoy!
On riding in frozen conditions: Obviously studded tires are only a help and will not work miracles. It will still be quite easy to wipe out if one turns or brakes too aggressively. Riding on snow, whether on roads or not, should be considered a form of off-road riding, and carries all the risks that entails. Techniques you may have learned for off road riding will transfer well to snow as well. In general a 'smooth' riding technique pays off. Pick lines to avoid soft slush and do not cross ruts diagonally; on bumpy snow it helps to raise off the seat a bit and weight the pedals, so as to keep steady weight on both wheels. Watch that rim brakes will be much less effective when wet.