Rethreaded Figure Eight 
There is more than one way of joining two ropes using a figure eight knot. The method described below is purely the one I prefer. One disadvantage of this method is that it leaves a bulky profile to the knot which could well get stuck when you pull the abseil ropes down. If speed and stuck ropes is a concern, perhaps investigate the double fisherman's method or the overhand knot (see below). The advantage of the figure eight with stopper knots over the double fisherman's is that it's often easier to untie afterwards, plus what I'd call a psychological advantage. Anyway, follow these steps to join two ropes with a figure eight knot:
Step 1: Put a figure eight in the end of one rope. Step 2 & 3: Rethread the eight with the end of the other rope. Leave plenty of tail (probably more than pictured), because the knot will slip a bit as it is tightened.
Step 4: Because I'm paranoid about the figure eight slipping I generally add a stopper knot to each end as well. The figure eight with stopper knots is my preferred method, however as I say, opinions vary.
Note: Avoid using the "Abnormal Figure Eight" (pictured left), which Bush Walkers Wilderness Rescue's research shows to be dangerous. They state: "The Abnormal Figure 8 Knot is dangerous due to roll back slippage. It is possible that this knot when poorly packed and with short tails could completely undo with loads as low as 50kgs". See Also: Abseil Knots on Needle Sports, and this accident report on rec.climbing or R&I, in which such a knot may have killed a climber.
Double Fisherman's
Here's another way to join two ropes, the double fisherman's (pictured below). This method results in a smaller profile knot (should give less chance of stuck ropes) than the aforementioned figure eight method. Its basically just two stopper knots. Follow these steps:
Step 1: Put a stopper knot in the end of one rope. The trick with stopper knots is to form two loops, the second behind the first, and feed the tail back through both. Step 2: Before you tighten the knot, pass the end of the other rope through both loops as shown.
Step 3: Now form another stopper knot, this time with the second rope, wrapping your loops around the first line.
Steps 4 & 5: Tighten both knots and draw them snug against each other. Leave plenty of tail (probably more than pictured), to account for any slippage.
It's hard to describe in words. Be very sure you've got it right before abseiling down. I strongly suggest you get someone experienced to teach you this knot, in person, so they can verify you've got it right. The consequences of a mistake, when using this knot to join two ropes for abseil, are naturally going to be very serious indeed. Furthermore, its easy to stuff this up, especially if its cold, dark and wet and you're looking to bail in a hurry, so perhaps this is not the best method to employ, though it certainly works if done correctly. The knot can also be difficult to undo once you've weighted it.
Above Right: The double fisherman's used to join the ends of some accessory cord to form a loop, suitable for friction knots such as the Prusik, etc.
Overhand Knot
The overhand knot is probably the simplest and fastest knot you can form to join two ropes together for abseil. This can be very handy in situations where speed is critical to safety. It's also generally believed to be the least likely knot to get stuck when the ropes are pulled. But how scary does it look? Even with the recommended super long tails, the knot can take some getting used to.
The theory with this knot is that it will slide flat against the rock and flip over an edge rather than jamming. (See picture right, and check out Petzl's page explaining the concept).
Follow these steps to form an overhand knot to join two ropes:
Step 1: Grab an end of each rope and form the simple pass shown above. Step 2: Pull tight, leaving a large amount of tail (ie. about a metre) for both ends, to account for any slippage. It shouldn't slip too greatly if the ropes are of the same diameter, but this is not something to skimp on. You should probably leave more tail than the pictures above imply.
Note comments such as "The Overhand Knot should not be used on tape due to progressive cyclic slippage." and "There may be an issue with the strength of the Overhand Knot when used on older rope.", appear in research articles from the Bush Walkers Wilderness Rescue.
