My older two children (ages 4 and 6) have stools in their bathroom where they are able to wash their hands and faces before and after dinner. My 21 month old can climb the stool, but unless attended, this is discouraged. Otherwise we may find him on the counter bathing in the sink. This happened last month at my house with my friend's 21 month old....just wish I had the time to grab the camera, but I figured rescuing a teetering toddler hovering three feet over tiled floors was more important.
When my daughter was old enough to walk around, we taught her to use a cloth that I placed on a hook next to a little mirror on our kitchen cabinet below our sink. This would probably work just as well in a bathroom, but I liked to have him right next to me while I was cleaning from dinner.
My son had a hard time getting his cloth to stay on the hook so I added a little metal basket.
The basket was an afterthought and is just a suction cup metal basket soap holder for a sink but works great on the hook. (The suction cups are not in use.)
The little mirror I found for fifty cents at a thrift shop and attached it with heavy duty double sided tape. (The kind that's about an eighth inch thick). The hook is one of those plastic 3m hooks you can find pretty much anywhere.
It's fun for him to clean up after eating, and although he may need assistance with persistent oatmeal, he's getting pretty efficient.
....And a clean toddler is a happy mommy!