You do not need to remove the faucet to repair that leak...
The O-Rings on the spout are leaking...
Also does the faucet shut off properly? It's running in the picture and I was just wondering...
All of the repairing you need to do can be done from the top side without removing the faucet.
Of course it would help a lot if you/we knew the manufacturer because then you would know the right parts to get or, order.
This is a parts diagram showing a faucet somewhat similar to your faucet and it may or, may not be what you have.
http://www.moen.com/shared/docs/exploded-parts-views/87254pt.pdf
And here is another type...
Product Documentation : Customer Support : Delta Faucet
Once you get it apart seeing the valve mechanism or cartridge we may be able to say what it is.
Some mechanical skills will be required as neither of these are what you actually have and you will need to pull it apart without breaking anything...