What I do is heat the comb on the stove. When it's piping hot, I then dip it in a jar of relaxer (I use Bantu super strength). You should to do this outside because this process generates lots of smoke.
The buildup on the pressing comb will melt away. You then run the comb under hot water to remove any relaxer left.
I then take an old nail brush or tooth brush to clean between the teeth.
Finally dry it off with a paper towel and you've got a fresh pressing comb.
I can usually get three to four cleanings from one jar of relaxer.
Hope this helps.