Sooner or later you will probably run aground; almost everyone does. The most important first response is what not to do. Do not increase power and try to ram on through (you will just go harder aground). Do not go into reverse, rev the engine, and try to back off (you might stir mud and vegetation into the raw water intake or damage the rudder or prop). Instead, pop the engine quickly into neutral and drop any sail that is set.
Determine, first, whether there is hull damage. If so, and you risk taking on water, aground is where you want to stay for now. Why seek deeper water to sink in? Try next to learn the water depth all around. If you have a dinghy, use that to take soundings. Otherwise send out a swimmer (wearing a PFD of course, and perhaps trailing a line back aboard) only if the water is warm and it is safe to do so.
safe to do so. Once you know which way deep water Lifting off lies, use one of three methods to refloat. Easiest and safest
Lifting
offOnce you know which way deep water lies, use one of three methods to refloat. off Easiest and safest is to let the rising tide lift you off. This works only if there is, in fact, some rise or near high tide. The next best choice, if not hard aground, is to try reducing draft or tilting the boat. Emptying water tanks is an option if you can soon replace the water or are certain you can do without it. Emptying the holding tank is probably illegal but might be the lesser of two evils. Shifting heavy gear about the boat or into the dinghy can help in a small craft.
Tipping
offIf you cannot raise the boat enough to free it, drop an anchor well off on the side you want to tip towards, either using the dinghy or floating it out on a PFD or fender. A peek at the keel might help to choose the correct direction to tip, particularly if you have goggles or a face mask on board. If you use a dinghy, lower the anchor into the water and lash it dangling from the bow rather than trying to toss it out from within the dinghy. Make a loop in the rode, shackle the main halyard to it, and use a winch to pull the masthead downward and outward, toward the anchor.
Kedging
offThe last resort is to kedge off. Drop an anchor, this time, in the direction of deep water and as far from the boat as the rode allows. Depending on circumstances, this might be the same place as for tipping off. Put the rode on a sheet winch, apply as much strain as you can, and cleat it off to give it some time to work while keeping all crew well away from the tensioned line lest it break and snap back. If there is a second boat that can pull you off, stay mindful that an incompetent tow can further damage your hull, prop, or rudder.