DK = practice!!! And lot's of it ... and practice getting up into DK on land, in the pool and while you're waiting in between waves --- see how long you can maintain your balance on DK just in the water. Obviously the more time you can put in on the DK stance actually riding the better but if you go for an hour surf just think about how much time you actually managed to spend riding DK - not much I guess!!! So if you want to get better then do a few things to help improve your balance while you're not riding waves.
Your stance --- this is why I say practice on land .... slap your board on your bed or carpet and practice getting up and then look down at your stance - is your stance how you think it should be? Does it look like you have set-up like your favourite DK pro or local ripper? Is your back knee close to the rail edge with your fin off the tail which is important for stance as well as the fact that your swimfin acts to some extent like a surfboard fin - more so when you're riding forehand. And has your front foot positioned correctly? Some guys ride with it fairly far back - doesn't look the prettiest but it may work for them - but the typical stance places your front foot around the same distance from the nose as where your elbow sits when riding prone. And if you're on your forehand then turn your foot 'slightly' inwards - it may be a style thing but I also found this forces you into a good stance for forehand and on the style side stops that terrible fin hanging off the side look.
I see Sean just replied but I'll still throw in my 2 cents and you guys can pick up what you think works for you and ignore what doesn't. Sean is absolutely right about making sure you're not "sitting" and that you do need to drive weight into your knee so that you are actually burying your rail when you turn otherwise you will just skide out - this is essentially what you may be doing wrong. On backhand bottom turns you might want to grab your outside rail to help a bit when you are starting but don't get into too much of a habit. On big/late backhand take offs you may want to hold onto the rail into the bottom turn but generally release as you're driving out of it so you can adopt a more upright stance. Here's Brandon with two pipe drops on his backhand - on your backhand the rail grab is functional and stylish on your forehand it is neither though.
One thing I reckon though is that stance is vitally important and guys can't always pick that their stance is 'messed' up. But if you do want to progress then you do need to analyse it and it may be as simple as holding the cricket bat wrong.
So here's the important bit ---- you practiced on land and that was way easy to get up into the right stance --- so now take off on a mellow wave and when you're trimming comfortably look down at your board and take a look at your stance --- is that the same as how you were practicing? Is your knee, front foot and back fin correctly positioned? Are you upright or too crouched? It's a weird perspectice looking down but I found it helped me correct myself and still find myself doing it when I've got up and just doesn't feel right.
You don't have skegs on DK so it is important to learn how to drive off your rail ... you start off small ... learn to do small controlled bottom turns and carves and progress bigger and bigger ... when you start to do the really big ones it is all about
confidence --- go into them with all the power you want to put into it and be confident that you are going to be driving out of that huge bottom turn or snap - don't just think about the move but also picture yourself coming out of the move. And if you are doing turns or snaps then you do want to initiate them with your upper body starting with your head ... if it's a small turn then it is not so noticeable but big turns or snaps - watch the guy who has really got these down .... the turn starts with his head -> shoulders -> arms -> through the hips -> legs into the snap -> bring the board around back under the head position but his head is already looking down the line and the board needs to switch rail and 'chase' the head. Just like prone - the head always goes first!!! But ja - watch skating, snowboarding, surfing --- it's all the same ...
Finally - two last important things for DK:
1. You can wax your board as much as you like but make sure your fins are a decent soft rubber on the foot pocket otherwise you will not get the grip you need.
2. Make sure you're correctly riding goofy or natural if you're just starting out. I ended up Goofy by accident because back in the day there was not really anyone decent to learn from where I'm from and the only guy who thought he knew anything told me that you ride goofy on lefts and natural on rights. Good thing there were lots of lefts when I started out. Anyway - it may not be what everyone reckons but there are exceptions and if you're like me then you will want your strong, "control" foot up front. Snowboard/skate and I'm natural - control/power needs to be at the back but DK is different to these two sports. With DK my view is that because you're on your knee you're not doing much that your weaker leg can't handle and there is way more advantage in having your power/control foot up front where you can actually make use of it. This may not work for everyone and you do need to go with what will work for you in the end. (disclaimer ends

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Anyway guys ... enjoy!!!
Start small and get the technique right.