Materials needed: sanding block, medium grit sandpaper (about 400), semi-gloss enamel paint, some paintbrushes, lots of spare newspaper.
First of all, took everything outside and using the sandpaper and block, sand off all the clearcoat to get to bare wood. Wipe it off using a damp disposable cloth to get rid of all the dust. Wish I had a "before" photo for this project, but looks like I forgot!
Took it all back inside to paint, covering the floor with newspaper. Would be better if you could paint it in your garage though, as the enamel paint fumes aren't good for brain cells. I bought a little pot of semigloss enamel paint (usually used for your skirting boards, window frames etc) and some cheap brushes, and had a go slopping the paint everywhere. Didn't aim for a good finish, since the aim is to make the final product look slightly worn.
Don't paint the inside wood runners as either the drawers will bind, or you won't be able to get the drawers in at all if there's a fine clearance. Didn't bother painting inside the drawers, but you could if you wanted to. Let things dry off, and keep the dog away from it all.
After a day of drying, put it all back together. You could also have removed the doorknobs first, and replaced them with some other style - same with the legs. Actually looks pretty good in real life!
To get a really distressed look, you would now get your sandpaper and file away at the corners and edges to remove the enamel paint. However, if you wanted a really good (non-distressed) finish to your project, you should probably coat the wood with a primer prior to applying the enamel, and use a spray gun with multiple fine coats to get an even finish, since it's impossible with paintbrushes.
Anyway, this was a nice way of preserving an old bit of furniture and making it fit in with our new house.