(Enter the pro-active moderator, for cryin' out loud. However, I believe the conversion of an old dryer into a fur tumbler is most distinctly
a trapping topic.)
If it is of interest to anyone, 220 volts is the potential difference between the two 110 lines that come into your house. The potential difference between either one of these 110 lines and the neutral line is 110 volts. It's not really a conversion process, with 110 you are just using half of the 220.
Now, I can all but guarantee you that the motor that that turns the drum in your dryer is 110. I am assuming that you want to replace the 220 cord that is on the dryer now, with a 110 cord that can be plugged into any common outlet. I can't help you with that, and I'm not sure that anyone around here can. And frankly, I'm not sure how far I would want to follow "electrical advice" that I received from a trapping forum.
Best thing to do is consult with someone who for sure knows what they're doing -- like an electrician.