First of all, you should make sure that your coins are ancient or antique before cleaning them. Take these coins to a professional who will let you know the real worth of these coins.
Then you need to verify the type of ancient coins that you have in your possession. Try to check the details engraved on the surface of the coins including the year and date mark which will help you in determining that which coins belong to ancient period.
Now take the coins to a sink and rinse them by placing under the running water. Make sure you have placed sink stopper in place which will help in stopping the coin from going down if it slips from your hands.
You should only rinse the coin while putting it under running water. Do not rub the coin as it can create scratches on its surface which will decrease its original value.
After rinsing the ancient coins under running water, you should put these coins into a bowl of white vinegar. You should wait for at least ten minutes which will help in getting these ancient coins clean from dust or dirt.
If you observe that the coins are not fully cleaned yet, then repeat the process for one more time by keeping these coins under running water and put them back in the bowl of white vinegar and wait for another ten minutes.
Take out the ancient coins from the white vinegar bowl and dry them. You will observe that all or a major part of the coins has become cleaned.
Take a magnifying glass and check if there is still any dirt left on the coin. If you find, then take a cotton stick and clean it from the surface.