I'm looking for a cheap and easy way to refresh the look and finish of kitchen cabinets.

There are some products at Home Depot like the link below.

Watco 1-Pt. Rejuvenating Oil-66051H at The Home Depot

I am not familiar with that. Does it work good?

Some cabinets look fade due to water and usage (see pictures below)

Thanks for any advise.

 

Wrong product for that.
That would be for bare wood that only has an oil finish on it.
Yours are sealed with shellac or poly.
To do it right I would number them on the back side on a piece of blue painters tape, remove the doors so you can work on them laying flat, clean with TSP, rinse and let dry.
Reason being is any sanding would tend to just grind the grease into the finish.
Sand with a fine sand paper to remove any loose finish and give the new finish something to bond to.
Clean again to get all the dust off.
It needs to be 100% clean!
Apply new poly with a quality natural hair brush, let dry for 24 hours.
Lightly sand again, clean and apply another coat.
The more coats you take the time to do the longer it's going to last. One coat will be a waste of time.

 

I agree; clean, sand, remove the dust and apply poly. 2 coats will probably be sufficient but you won't know for sure until the 2nd coat has dried. I normally remove the hinges and take a magic marker to number the doors behind the hinge..... in case you need/want to freshen up the backside of the doors too.

It would be best to use an oil base poly! Water base poly will require a more sanding and won't give as hard/durable finish as oil base does. You also can't use a natural bristle brush with water based coatings - harder to hide the brush marks.

 

Problem is they seem to live in CA where they may not be able to even get oil based because according to them like everything else on the planet it may cause cancer.
How to Finish Wood - Wood Finishing Guide | Minwax
I missed where they live in the first post.