Best tutorial I've seen for wainscoting for your playroom. Use 1/4" MDF. Buy 4'x8' sheets and have Lowe's cut them into strips the width you want. No problems with warped boards and much cheaper than wood. @Jenny Freehardt
Inexpensive Board and Batten Wainscot How To
I think this is the wainscoting I will go with in our dining room and possibly entryway. Great DIY walkthrough with pictures. Should be easy and relatively cheap
DIY Classic Wainscoting Tutorial
Colonial Wainscoting Measurements by SnazzyLittleThings.com More
This is faux wainscoting done in a few hours and at a cost of $35! Could add this to the built-in benches in the kitchen...
A step-by-step DIY tutorial on how to EASILY install wainscoting anywhere in your home! If I can do you, I promise you can too!
27 Easy Remodeling Ideas That Will Completely Transform Your Home (On a budget!)
10 Cheap Ways to Make Your Home Look More Expensive
Emily of Decorchick! used a chair rail, wooden frames, caulking, and several coats of white paint to create this wainscoting look-alike. Get the tutorial at Decorchick!.