If you find a cistern in your basement and simply don't want it there, your primary option is to fill it in. This usually involves emptying the cistern of all water, sealing it, then filling it in with concrete or other materials. You may then be able to cover the cistern up with flooring materials, depending on the size and shape of the cistern. A tank cistern may need to be taken apart and removed piece by piece.
Your old cistern may have already been blocked. Unfortunately, old cisterns may not be blocked correctly. Many are just covered up or hidden. This is a mistake, because it can lead to mildew problems, moisture leakage and structural difficulties. If you have a cistern that hasn't been fully sealed or filled in with concrete, you'll need to seal it properly to avoid future problems.
Cisterns were designed to store water, and you can still use your cistern for this purpose. The space is already there, so you may be able to install steel casing and use the well to continue to keep and draw water. If your cistern is old or unused, you may need to install a new pumping mechanism as well as sealing it and connecting it with the plumbing you already have.
If you live in a moist climate, rainwater collection is a popular use for old and otherwise unwanted cisterns. You can attach gutter pipes or other collection devices to a cistern to channel the rainwater inside. Then, if the attachments are not already in place, you can hook the cistern up to a simple spout outside your home for gardening water, which can save on water bills.