A 12-volt rechargeable battery is the lead-acid type normally used in cars. If the battery is simply run down, you can fix it by recharging it with a charger approved for lead-acid batteries. If the battery won't accept a charge, it's probably due to sulfation. This occurs when repeated deep discharges cause sulphur to coat the lead plates in the battery. This problem can be fixed inexpensively if the damage is not too severe.
Use a crescent wrench to disconnect the battery and remove it from the vehicle. You should wear safety gloves and glasses and work in a well-ventilated area because the sulphuric acid in the battery can cause serious chemical burns. Remove the plastic cell caps (located on top of the battery). If it is a sealed battery, locate the markings on the top of the battery that indicate "shadow caps" and drill through them to open each cell.
Test the battery to see if it is salvageable. Use the voltmeter and a wire probe to check each battery cell. Insert the probe into the first cell and write down the voltage reading. Repeat for each cell and add up the readings to find the total voltage. Provided the total voltage for the cells is still at least 10 volts, you may be able to fix the battery (though 11 to 12 volts is better). If the battery has degraded beyond that point, there's little chance of repairing it.
Make a solution using a half quart of distilled water heated to 65.6 degrees C and 7 or 8 ounces of Epsom salts. Do not use tap water in a lead-acid battery because it may contain chemicals harmful to the battery. Drain the battery acid fluid into an acid-resistant container (glass and most plastic will work). Neutralise the acid by adding baking soda slowly, a tablespoon at a time, until the fluid does not bubble when you add more soda. Pour the fluid down a drain and let water run into the drain for a couple of minutes to flush it. Use a plastic funnel to fill each cell with the Epsom salt solution. Shake the battery to make sure the solution is well distributed.
Make sure the battery charger is turned off and hook it up to the battery. Connect the positive lead to the positive battery terminal and negative to negative (the positive terminal will be marked with a "+"(plus) symbol and the negative with a "-" (minus). Use a 3-phase ("smart") charger designed for lead-acid batteries. Make sure the voltage is set to 12 volts. This type of charger will automatically switch to trickle-charge once the battery reaches full charge, preventing a damaging overcharge. Turn the charger on and let the battery charge overnight.
Turn off the charger when charging is complete and disconnect the charger leads. Replace the cell caps and reinstall the battery. For sealed batteries, close the drill holes with plastic plugs (you can get them at an auto parts store). The battery should now function properly. It's a good idea to repeat the charging process in a day or two to make sure the Epsom salts have removed all sulphur from the lead plates so you get maximum performance.
Sulfation causes permanent corrosion of the battery plates. Repeatedly running the battery down will cause more sulfation and eventually corrode the lead plates and ruin the battery. You can fix any lead-acid battery using this method. However, if the battery is used in a golf cart or other device that is stored for long periods, you can extend the battery life by removing it and placing it on a conventional or solar trickle-charger.