I paint furniture all the time, and if this is your first DIY, it sounds like a large undertaking. But it can certainly be done.
The prep work is very important. I would do a light sand and cleaning, then prime with an alcohol or oil based primer, like BIN or Zinsser. You can use a water-based primer, but since you have cherry and it was probably waxed, I'd go for the BIN, which is smelly, so work in a well ventilated area.
Next step is to paint. You can use latex for this, and there are many options. You can use a brush or a roller or a combination of the 2.
After you paint, you can sand the edges to reveal the wood underneath for that distressed look.
Then, you can glaze it or seal it.
If you could post a picture, that may help others, and try posting this on the home decorating forum. Lots of DIYers painting their own furniture!