A single handle faucet that leaks around the base may be an easy fix or you may be replacing the faucet. If it was a kitchen faucet, I would replace the o-rings, but the difference is a bathroom faucet is that the spout doesn’t swivel, so those o-rings don’t exist. There are a few things to look at though.
See if you can tell where the water is coming from. In many cases, the water will be traveling from the aerator, down the underside of the spout and finally puddling around the base. If this is the case, remove the aerator and either clean it up and reinstall it, or just replace it.
Another possibility is that water is coming from around the handle. In this case I would replace the cartridge. You will need to turn off the water, remove the handle, remove the retaining pin and finally pull out the cartridge. Get a replacement and reinstall it.
Lastly, it may be that the faucet is corroded and needs to be replaced. You may not even see the leak from above. The body of the faucet may be corroded and pitted or cracked and you may not see it. If you can’t see the leak, you probably are looking at replacing the faucet.