The key to standing in a kayak is confidence. First, start the following exercise by KNOWING that you're going to end up in the water!
Put on swim trunks, a t-shirt and a PFD. Leave your fishing gear behind. Bring a buddy in his/her kayak to assist if necessary. Paddle out to open water, stand up and start moving around. You will probably find that it is easier to stand and sit back down from a tall seat. The use of a strap or bar to assist until you get the hang of it is helpful.
Test the limits of YOUR balance and get a feel for the stability of the kayak. You will never know how far you can go until you figure out exactly how far too far is. Yes, you'll eventually end up in the water, which is the point. I think you'll be surprised by how far you can go and you will develop better balance with continued practice. Many times the issue is not the stability of your kayak, but YOUR stability. The way to develop that is to keep practicing. You will also have confidence in the ability of your PFD to keep you afloat and peace of mind is a game changer!