Start by sanding the wainscoting with a 150 grit sandpaper. Random orbital sanders work great for this, but might be over-kill. You're not trying to remove all of the old finish, but to scuff the surface a little and remove any dirt or grease on the walls. The most important thing to do is use a sealing primer next. I use "Kilz" and it always gives me good results, (smells really bad though). You have to do this to seal the wood, so no oil, sap, ect... bleeds through. After the "Kilz" has dried you can paint it as normal.

Some "Wainscoting", the type with the grooves, can be a pain because it's hard to get the paint in the cracks, so when you're picking up your paint, buy a roller with a large "nap", usually used for painting concrete or brick.

Good Luck!