Painting Furniture

Is this a synthetic type finish or a wood shelf?
You need to sand it first. So that the paint can grip onto it. Then use a primer. Then paint it.

Or, ask the guy at the hardware store, what paint to get and how to prep the surface before painting it.

Acrylic Enamel, is a glossy paint.
And it will slip off. So you have to prep the subsurface of the shelf first. Then paint it.

You need to start over.
Sand the shelf.
Prime it.
Then paint it.

Did you sand it down very well? You either need to sand it down (not all the way, just enough to rough up the surface), clean it with a tack cloth, or get a non sanding primer, one that has grip, otherwise the paint will slip like you mentioned, or it will peel off when dry.

So, I would:
1. sand
2. use a primer
3. paint (or use a two in one primer/paint)
4. seal

If you want a glossy finish, you can get the enamel look paint, a high gloss paint, or you can seal it with non-yellowing polyurethane.

There are tons of online tutorials that can give specific brands, here are a few good ones:

http://www.centsationalgirl.com/2010/11/credenza-practica...

http://www.thenester.com/2010/07/how-to-paint-furniture-l...

(this is in a series of 3)
http://www.inthefunlane.com/2012/01/paint-perfection-clas...
http://www.inthefunlane.com/2012/01/painter-perfection-cl...
http://www.inthefunlane.com/2012/01/paint-perfection-clas...

Did you strip the original paint or sand it in some way to give it some texture?

Sand it first. That will give something for the new paint to hang on to. If you want to test first, sand somewhere out of the way like the bottom and paint just that part.

You can't put enamel over latex and vice-versa without a primer. And you probably need to "rough up" the finish with sandpaper.

OneandDone is right. Scuff it up a bit and use some primer.