One of my relatives sent me this calling card in the mail after I told him that I have very little Verizon minutes, and I just wondered if it would work with my Verizon cell phone (we don’t have a land line) or not.
On the back of the card it says to use it with a touch-tone phone (which I’m assuming means land line), but I can’t find any other info on it.

Most any calling card will work from a cell phone.
Problem is, even if the calling card has a free local area access number, or 1-800 access number, your cell phone will still charge you airtime for the connection. (unless you are already paying for unlimited airtime, or x number of free minutes/month).
But, yes a cell phone is the the same thing as a touch-tone phone. They send the same DTMF tones as a landline for dialing and vertical service signaling (* codes, etc).