Removing a faucet should be a fairly straightforward process. You may find, however, that removing the plastic nuts that secure the faucet to the sink can be a lesson in futility. Over time, even these plastic nuts will become very hard to remove due to rust on the threads. Using a regular basin wrench is not an option due to the "fins" on the side of the nut. Use those "fins" to remove the plastic nuts and finish your faucet replacement project.
Slip a pair of pliers between the fins on the nut. Position the jaws of the pliers so one jaw is on one side of a fin and the other jaw is on the opposite side of the remaining fin.
Grab the handles of the pliers with both hands and turn the nut counter-clockwise. This should give you enough leverage to start the plastic nut moving until you can unthread it by hand.
Consider another option if the pliers don't work. Set the blade of a short flathead screwdriver against one of the fins. Position the screwdriver blade so it's at the joint between the fin and the side of the nut.
Tap the screwdriver handle sharply with a hammer. This will be more than enough force to get the plastic nut turning.