In the Czech Republic people will usually have a washing machine at home so you will not see a laundry shops very often. The easiest way to deal with this problem is to hand over your laundry to someone at a hotel If you are staying in Prague city you can find there a few laundry services as well.

The first self service laundry in Prague, Laundry King, is located near metro station Hradcanska (many ex pats are frequent visitors here):
Dejvicka 16, phone 233 343 743 or 603 713 855
Another laundry, Laudryland Praha, have five locations:
Londynska 71, phone 222 516 692
Vinohradska 50, phone 224 253 117
Chrudimska 2, phone 272 743 981
Na Prikope 12, phone 221 014 632
Plzenska 344, phone 257 310 021
Delivery service available at 603 411 005