I love my alum block and I have been using one for a number of years. They last forever, but you don't get to drop one on tile but once maybe twice! They really will cool down burn and help to condition your skin.
As stated above a rub on your fingers will help you to stretch your skin wihtout slipping.
After a shave I rinse / wet towel wipe then wet the alum block a little and wipe it all over. Go brush my teeth, etc. and rinse off with cold water followed by an aftershave balm and follow up with my favorite aftershave.
There is a local Indian grocery that sells a block of alum in the shaving section for $2.99 and the cheap cardboard box says "Nice Cool Alum Block". At that price you can afford to drop one every now and then!
I hope that helps.
Will N.