Charleroi used to be a bit of black hole in that when you went into the city, you never seemed to be able to escape, going round and round in circles.
As to transport, Charleroi train station is right by the airport and there are direct trains to Brussels, even further away from Gatwick is to Victoria.
There are a few train station stop in Brussels do you know which you are going to? Gare du Nord, Gare du Sud/Midi and Centrale, also Louviere as well.
The shuttle bus is the easiest way to get to Brussels from Charleroi airport. The shuttles arrive in Gare du Midi (Zuidstation in Flemish), and from there you can take a metro or an underground tram to most of the places in the city. The metro map can be found for example here:
http://www.bxel.net/metro-de-bruxelles/plan-du-metro.html
There have been changes in the metro network lately, so be sure to check the latest version of it, the one with metro lines with numbers 1-6.
One word of warning: if you arrive late in the evening, remember that the public transportation runs only till around midnight. There are some nightbuses, though, but the network of them is not very complete.
nyway, my advice would be to avoid wandering by foot around the station areas at night time, as that might not be the safest thing to do...you may want to taxi and stay locally overnight.