tile on old countertops

I want to lay ceramic tiles on my countertops which are covered with what looks like linoleum or something similar from the fifties. What do I have to do or use in order to tile over this material?

It would be better to do remove the old counter top and start anew, but if you must do it your way: sand the top cross hatch with 80 grit sand paper, wipe it down with acetone, prime the entire surface with a thin coat of mastic, wait 24 hours, then tile away.