There's a ton of material on this online.
Hey Iron man, I need your help about setting up armbars. How do you separate your opponents arms when he is griping his gi or his hand to prevent it, especially if he grips it tight?
It's a regular position, you are on his side, you've positioned the legs and got your arm underneath his elbow. How do you break his grip? If you can find some video instruction I'd be very grateful too.
Ari Bolden has a really cool trick called the Silverado.
Personally, though, I have two attacks on the arm that I like to use.
The first is one I learned from Steve Maxwell, but I try and avoid it a lot of the time because if you finish it as an arm compressor, then it can get you DQ'd.
The move is pretty simple, though. Gable grip so that your thumb and the top of your radius is digging into his bicept, take your bottom leg and lay it flat (so that the side of the shin and the calf are down) against his wrists or the far forearm. Lean back and tighten up the pressure.
This is, actually, a bicept slicer and that will force him to release the grip or to tap (verbally, usually, because he can't move his hands). The fact that it's a bicept slicer is what makes it illegal in a lot of competitions, but I rarely ever finish with the slicer if I apply the pressure slowly with the legs. If you apply it quickly and tighten the legs up, it's really easy to force the tap with the slicer.
Some guys are smart and will let the hands break and try to roll out.
There are two ways to beat this:
1. Hammer down with the top leg. This is actually a good way to start the move initially, and it prevents the roll up because it keeps pressure on the neck. This has a risk, though, of letting an opponent with strong hips roll up on you.
2. Transition to the triangle. As they roll up, remove the top leg and twist to the side to hook their leg (preventing the slam) and setting up an appropriate angle. This is one of my favorite moves, personally. I like setting up the triangle from the top, as I find it's a lot tighter.
The second way of freeing the arm is one I picked up from watching Demian Maia and actually asked Royler Gracie to help me with at a seminar (which is why this description has some details you won't hear from most instructors).
It's a lot easier to free the arm when the elbow is up. It's away from their core and it makes it difficult for them to effectively use the pecs and back to defend the submission, making for better control. Even if you have the bottom leg in, you'll notice that they can still pull the elbow down, often into the thigh of whatever leg you have across the body. This doesn't help them escape at all, but it makes it harder to finish the armbar.
A lot of guys try and attack the wrist when they get to the position you described. As Royler pointed out to me, if you watch the guys who are really good at locking in the armbars off the top, and making people tap fast, they actually attack their opponent's elbow.
Use your top hand to hook under the elbow and pull it up towards your top leg. Keeping your knees pinched together and your heels pressing down will keep them from bridging up and into you, knocking you over. When you've opened the elbow, then you can lock the elbow in place with your bottom arm (hook under with your forearm and keep the knees pinched to control the position, grabbing your own lapel with your bottom hand), then move up to the wrist with the top hand.
Don't pull the wrist up and yank at it. That's a waste of energy.
Instead, control the wrist with your hand and rotate your upper body towards your opponent's head. Keep your hips down and heels pressing towards or into the mat to make sure they don't bridge into you. Rotating with the whole of your upper body and in a twisting motion will make it really hard for your opponent to hold on and liberates the arm pretty easily.
Personally, I use the first method and then, if I get frustrated, I move to the second, which is more sure-fire and a little more brutal.
EDIT: Damn this was a long post. Hope that was helpful.