Determine what the faucet has for internal or external hardware at the outlet. Unscrew the drop-down outlet, if present, using the channel locks or pliers. If there is no drop-down present, determine whether there are internal threads in the inside of the outlet of the faucet.
Look into the outlet of the faucet to determine if the drop-down was attached to external or internal threads on the faucet head. If there are external threads, you can most likely attach the filter base to those threads. If there is a regulator, you may need to remove it to insert a drop-down plumbing thread for the base to screw onto. Ideally you would have already taken the faucet apart to determine what you need before shopping for the water filter and base.
Wrap pipe tape or thread seal around the threads of any adapter you may need to apply to the faucet and tighten them securely to the faucet head. If there are external threads present on the faucet head, you can most likely skip this step. There will be an internal gasket on the water filter base that will prevent leakage when screwed on tight enough.
Screw the base onto the faucet head or adapter tightly.
Insert the water filter into the base per the directions that come with the filter and base.
Read the directions of the water filter and base. There may be a priming period for the filter where water will need to be run through it and discarded. On many water filters there are indicating lights that will tell you it's working properly and when it expires. When the filter does expire, you most likely only need to replace the filter and not the base, but may need to re-prime the filter all over again.