Dear Town,
The best way I've found is to use either a flat shovel or an ice chopper. Jam it under the strips and lift. Caution!!!! Those ****ers are sharp!!!! Use gloves to handle the tack strips and for goodness sake watch where you kneel!!! I knelt on one of those @#$%^&&*( things and it stayed with me and hurt like h e double hockey sticks. Also look out for left over razor blades that some idiots leave in the padding.
Good Luck,
Len

Hammer and a wonder bar (flat crowbar) is how I have done it. I have tried alternatives so as to prevent chipping, but they were not strong enough to lift the nails out of the cement. The nails are shot in the concrete with a gun, and designed to hold strong enough such that you will need to chip the concrete to get it out. Otherwise, they would not hold the carpet in place.

Nonetheless, a hammer and a wonder bar suffices.