DISCLAIMER: generally, it is the inexperienced folk who need the most advice on this kind of thing. however, some 'techniques' described are dangerous, decrease your safety margin, etc, so might qualify as the sort of thing best applied by experienced climbers. if in doubt, for f*cks sake- stay on the ground or walk off!
1) Use the EDK to tie two rappel ropes together. (Euro Death Knot. Death* Knot. Overhand. Whatever you call it works fine). It rides over rock features infinitely better than the old school knots, and conveniently is a hell of a lot faster to tie and untie.
*Why is it called the 'death knot'? Because if you f*ck it up you could die. Unlike the rewoven figure eight and fisherman's knots, there is not much margin for error with the EDK. The EDK, tied incorrectly, DOES fail at loads that could be achieved while rappelling.
To tie the EDK, put the two ends of the ropes together. Tie them in an overhand (pretzel) knot with a good chunk of tail. I use at least a foot and a half. Other folks use other lengths. Just don't let it be short, as the knot fails by rolling over itself again and again towards the end of the rope. Nice to have a little margin there. Do not tie a figure eight knot, as it can roll at lower loads. Then make sure the knot is 'dressed'. That is to say, all the strands lay flat and parallel. There should be no kinks or twists in the knot. Then set the knot. This does not mean just grab two strands in each hand and yank. This means take each individual strand (there's four) and pull hard on it, one at a time. If you are unsure of what all this means, tie one and see if it makes sense. If you still arent sure, look up some pictures online or find a kind and enlightened climbing friend to show you.
2) Know which rope to pull. You can't pull an EDK in standard diameter ropes through a rap ring. A lot of climbers get overly worked up about this- it is usually immediately and readily obvious to even the dimmest climber when you are pulling the wrong rap line. However, in the rare case that you are rapping a really high friction face, it is nice to know that the reason the rope isnt coming down is because of the friction, not because you're tugging on a jammed knot.
This would probably be an appropriate time to mention that you need to be sure there are no knots in the end of the ropes when you are pulling the rap lines. Funny how often this seems to happen, and overhands, figure eights, slip knots, and other monstrosities have an odd habit of tying themselves in the ends of ropes when no-one is paying attention. Keep an eye on the end of the rope until it is out of sight/reach.
3) When you begin the rappel, make sure there are no twists in the rope above your device. When you end the rappel, do not let the ropes twist together before pulling. The additional friction can make it that infinitely (or impossibly) harder to pull a rope over featured, high friction, or slabby terrain. Yet worse, if you have a twist in the top of the rap, and the rope sits in a groove, the pull strand may become jammed when the knot tries to pull through but is pinned by the slack strand.
4) On windy days, wait to toss your rap line in lulls in the wind, or better yet- rappel with it. To do this, either pack-flake it into a backpack and just let it out as you go, hang the backpack off your harness beneath you, or flake it over a sling and hang that off your harness (the latter is faster, easier, but more likely to make a mess). Either way, you pay it out as you go. It takes longer, but it beats the hell out of throwing your rope and watching it wrap around the tower, only to get stuck on a chickenhead that is impossible to rappel to without a life (and/or ego) threatening pendulum/tension traverse/unprotected climbing/etc . Add wind noise, and it gets hairy. Believe me.
5) Consider rapping without knots in the end of your ropes. If you are rappelling very catchy featured rock, occasionally the knots will hang up somewhere on the toss that is tricky or impossible to get to, or to get unstuck. If you understandably want the safety margin that knotted rap lines provides, consider a rappel backup instead, which I think is a more logical safety measure anyways (If you drop the brake lines, would you rather stop immediately, or at the bottom of your rope?). Just pay attention to where you're going when you're near the end of the rope.
6) Watch the rope line. As you rappel, examine the rock you pass over. Are there cracks in it that will eat your rope? Chickenheads? Upwards facing flakes or slots? Pieces of old cut rope sticking out of a crack? Bushes? Cacti? All these are rope eaters or destroyers, and if possible, it would be nice so that when you pull your rope neither strand goes near them. Sometimes they are impossible to avoid, but generally you can do something with the rope as you rappel to keep it away from the rope-eater, using rock features to redirect the rope above you like putting your rope in a friendly groove or hooking it around a chickenhead to keep it away from the bottomless creaky flake which has seven frayed rope pieces sticking out of it.
7) Seal off rope eating cracks, if possible. I've had some success defeating otherwise ravenous upwards facing rope slots and flakes by lodging a few small rocks in them on the way down, or more normally, examing the rope-eater on the first rappel, and telling the second rapper to bring down some appropriately sized rocks/sticks/etc with her.
8) When there is a shelf, incut rock feature, constricting crack, ledge, or other obstacle that is likely to hang up the knot near the top of a double rope rappel, you would do well to clear the knot on the way down. This requires some fiddling, and wont work if you need to rap the full 50m, 60m, whatever it is that you are rapping. To clear the knot, rappel past the obstacle and stop at a convenient place where you can unweight the rappel. A ledge is best, but clipping into a bolt or solid piece of gear will work if you keep your head together and keep your hands on the brakes. When you've unweighted the rap lines, start feeding the ropes in opposite directions through your device so as to move the knot down. If the knot does indeed look like it will catch, either flick the rope around a bit and get it below the offending feature without catching, or get back up there and do something else progressive. It is much easier to deal with a knot-grabbing feature when you are only six feet away, not at the end of your 200' rap and you can barely even see the knot, let along flick it out of the crack. When the knot is below the feature, weight the lines again and rap away. Again- this is generally only done for features near the top of rappels (like clearing the edge of a belay ledge, etc) because they are more predictable (you know pretty much where your rope will pull over the rock near the top) and because it would take really long ropes to be able to clear the knot a long distance and still have enough rope on the threaded line to reach the next station.
9) Test pull. After your first climber has rappelled, if there is any question about whether the rope will pull (there is a feature near the anchor which looks grabby, or there is a lot of friction), the first climber should do a test pull where they pull a few yards of rope through the anchor to see if everything is working the way they intended. This can also clear up whether knots will clear ledge edges and whatnot. If everything is hunky dory, just even the ropes out again and the second climber can come down without worrying about whether it will pull.
10) The time the rope is most likely to get stuck, particularly if you take care to watch your rope line while rappelling, is on the pull, where the last chunk of rope whips through the anchor and falls. In order to minimize it getting stuck on rock features, wrapping around bushes, etc, pull slowly and gently when the rope is almost about to pull, and then when you can feel it just about to fall on its own weight, give it an enormous yank and watch it fly out and away from the cliff on the way down. At least that's how it works when the timing is right and the planets are correctly aligned. (Actually, its a good thing to do, whether or not your planets are aligned). one note: this violent rope whipping motion makes it anecdotally more likely to knot a twisted rope around itself at the rings. if your rope is kinky, or the pull is so low-angle that there is no way it could fall to you with even a hard yank, then just pull it through gently and cross your fingers.
11) Stand away from the rock when pulling. Obviously not an option in the middle of a multipitch rap, but if you're on the ground, you would do well to stand at least a few yards away from the face when pulling the rap lines. It will help you see what is going on, will keep at least one rope out of the cracks, and gives you a better shot at getting the last-second yank to work out well.
12) In rope-eating territory, in the middle of multi-pitch raps, consider flaking the rope as you pull it down from each rap, instead of threading it at the anchor, or letting it hang below you. Although it is thankfully rare, ropes do get stuck beneath climbers, and I have the dubious honor of having had a rope stuck both above me and below me, which leads you with fewer options for retrieval of the top line. If you flaked the rope while pulling it, and the top line gets stuck, you have the flaked bottom line as your new lead line, ready to go. Some climbers get pretty psyched about saving time on multiple raps by threading the bottom line through the anchor as you pull it, but I think this is overrated. With the EDK, it takes seconds to untie it, and only a few more to retie it, so with awkward anchors its sometimes easier to just flake it in a lapcoil, untie, rethread, and retie the ropes while pulling, instead of muscling the entire rope through the frictiony rings while pulling. When the top rope falls clear- just toss the lap coil off the cliff and you're all set.
13) Another option for rope-eating territory is to switch over to single rope raps instead of doubles. Obviously not an option for most places, but some times there is the option to do an intermediate rappel for the one-rope teams which two-rope teams happily bypass. If its a catchy pitch, rapping on one rope means no knot to catch, and only one rope in jeopardy at a time.
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and once your rope is stuck? well thats a whole 'nother story, but two notes:
1) pulling with all your might is always the *last* thing to try. an act of panic or desperation. in some cases this will irretrievably fix your rope. bring a knife if it gets cold at night..
2) do not kill yourself attempting to retrieve the rope. it is embarassing and painful. just because a rope feels stuck, doesn't mean it's necessarily good enough to jug.