Different inks and materials will require different treatments after printing. Most fabric ink require you to use a clothes iron on the printed fabric after the ink dries, in order to heat set the ink so it won't wash out in the washer. Read the instructions for your ink to see what is required.
After you've printed, you can save your stencil indefinitely, but obviously you can't reuse the same screen for another stencil, without first removing the old stencil. The process of removing a stencil from the screen is called reclaiming the screen, and it's usually just a matter of applying a special chemical to remove the photo emulsion. Remember that once exposed, water alone is not enough to wash out the emulsion. Fortunately, a number of different solutions are available that will wash out exposed emulsion. Check the instructions for your emulsion to see what it recommends, but usually a low strength paint thinner will work, or you can buy a solution called Stencil Remover quite cheaply and this does the trick well. You simply pour a small amount of the solution over the stencil, rub it in, and then wash it out. The emulsion should wash out with it.
As an alternative, it is possible to remove a screen from the frame, so you can save the stencil and still have the frame available for new stencils. Stretch another screen over the frame and you're good to go. If you're careful removing the stencil, you should be able to reapply it to a frame at a later time if you decide you want to print it again. This way, you only need a few frames, but you can create a veritable library of stencils which you can reuse whenever you want.