The housing around your well water filter, or the filter itself, lists what brand your system is. If it's not on the housing of the filter, try checking the system itself. You'll need to know the brand name to ensure you get the right filter. Some common well water filtration system brands are Whirlpool, Reynolds, and Culligan. The model number should be listed near the brand name on your filter housing. There might be a label on the housing that lists the model number, or it might be stamped right into the metal or plastic of the housing. You can buy well water filters at most home improvement stores, or you can order them through online retailers. You can also check the website for the brand you have; they sometimes sell their filters directly. You can expect to spend between 25 and 35 dollars for your replacement filter, depending on the brand and model. A filter wrench is designed specifically to make removing old filters easy. Metal filter wrenches have a handle, usually coated in plastic or rubber, on one end. On the other, you'll see a large circle made of metal. It will slide over your filter. You can purchase a metal filter wrench from most online retailers.
Note the filter brand. Check the filter model number. Purchase a new filter. Get a metal filter wrench.