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..