The current Spa-Francorchamps layout has been in use since 2007. With the exception of a few pieces of track, it's the same course which has been used since the 1983 Belgian Grand Prix.
Most of the corners are named, and I'll attempt to provide a brief explanation of the origin of each.
A lap begins on the pit straight, one of the shortest on the calendar. Almost as soon as a car has crossed the line, it's braking for the very tight Turn 1—La Source ("the source") hairpin. Overtaking is possible here, but not too common—the preceding straight just isn't long enough.
However, if a car gets out of shape defending into the previous corner, the likelihood increases greatly.
The cars then head flat-out through a tiny kink for Turn 2, and downhill into a valley—home to one of the most famous corners in the world.
Eau Rouge ("red water" in French) is named after a stream that runs under the circuit at the base of the valley in which the corner sits. The water in the stream does indeed appear red, due to iron oxide deposits on the riverbed.
You can follow the course of the stream through the infield of the circuit on an online map service—there's a good one from Bing on Virtual Globetrotting.
Eau Rouge (Turn 3) is the left-hander at the very base of the dip and is followed immediately by an uphill right-hander called Raidillon (Turn 4). The final part of this awesome corner sequence is a left-handed flick (Turn 5) at the crest of the rise.
The challenge today isn't quite what it once was—modern cars have so much downforce that taking it flat-out is relatively straightforward. But it remains a very special corner (or rather, sequence of corners), and a mistake here will usually end your race in a hurry.
Next up is the longest straight at Spa, and another barely-there flick (Kemmel, named for a Belgian village) serves as Turn 6. Taking a better run through Eau Rouge opens up an overtaking opportunity here and under braking for the next corner.
This is the first part of a medium-speed right-left chicane (Turns 7 and 8) called Les Combes (which I believe is "the combination"). It's followed immediately by a medium-speed right (Malmedy) on the exit, pointing the cars onto a short downhill straight.
Turn 10 (Bruxelles) is a long, slow downhill hairpin which can easily catch out the unwary, especially on a slippery track.
Turn 11 is a quite straightforward, unnamed left-hander taken at medium speed, which leads onto a fairly short straight.
After this comes another of Spa's beautiful corners, the very fast double left-hander of Pouhon (Turn 12). I believe "pouhon" means "spring" (as in a natural water source). Spa is, after all, the original "spa town."
The first part is slightly tighter than the second, and the cars can take a lot of speed out of here onto another short straight.
Turns 13 and 14 are a quick right-left chicane called Fagnes, and they are followed immediately by a medium-speed pair of right-handers named Paul Frere and Stavelot (Turn 15 and 16).
The drivers now re-join the route of the original Spa circuit. It's flat-out through the left-hand kink of Turn 17 and the foot stays planted to the floor through yet another legendary corner, the left-hander of Blanchimont (Turn 18—named after a small village).
From here it's only a short run down to the new Bus Stop chicane, Turns 19 and 20. The chicane is slow and tight, and there's a strong likelihood that we'll see some passing here in the race.
The cars are now back on the pit straight, and it's a short run down to the finish line.
The pit lane entry is on the exit of the final chicane, and the exit is just after Turn 1.