The drip probably is a bad cartridge, would have to change out one or both of the cartridges, either the hot or cold, take off the handles to pull out the cartridges. The sprayer not working, either the hand sprayer itself is wearing out or broken, or there is a build up of scale in the spray end where the water comes out, or the diverter is going bad or scaled up and not working properly...diverter would be under the spout..Hmm..don't recognize the brand of faucet it is, would make trying to find parts difficult. maybe some of the other plumbing professionals that are on here (you know who you are) might recognize what it is. You may be better off just replacing the darn thing rather than trying to fix it. By the time you chase around town looking for parts, mess around with it and tear it apart trying to fix it you might as well just put a new one in. Try to go with a Moen or Delta, something that parts are easy to find.--TheCaptain

Don't see sprayer, but from the look of the photo, I suspect mineral-clogging.

If the faucet is dripping, that's likely one of the valves on either side. To find out which one, go underneath and turn off hot and cold supply one after the other. Wait a bit after each one. Whichever one makes the drip stop, that will show which valve is the leaker. However, if you're tearing into either one, i'd do both.

Without intending offense, from what the picture shows, I'd replace all....unless you're really enamored of this particular set-up. Looks like standard three-hole arrangement. New units aren't all that expensive. Many come with pull-out-from-the-spigot spray heads that you'll likely find more convenient.

Thank you for the advice. I am definitely not enamored of this and would love to replace it - spending money is an issue but if it could be done inexpensively i might go that way. Thanks again.

Search using the term "faucet aerator" and you'll see what you are calling "spray". If you can unscrew the aerator, you can clean it. The existing one. You can also carry it to a hardware store and ask them to spot which new aerator take the same threads, buy it take it home and screw it on. A new aerator. It might have a swivel ball joint so you can direct the stream around in the sink.

http://spring-flo.info/services/faq_answer-details.asp?FAQID=13

http://www.ehow.com/how_5803509_shop-faucet-bathroom-faucet-aerator.html

Since you have two handles, each stream (hot and cold) is controlled by its own valve. One of the two is leaking. Which one? This is the valve to work on. Taking a picture of it, and posting it on a forum where many plumbers hang out, will give you free feedback on
1/ what you could do to adjust something where it sits in the "body", or
2/ how to buy another valve.

hth

Hi, no I"m not talking about the aerator; i'm talking about the sprayer which is not in this picture. thanks

With respect....that looks like a nice big stainless combi-sink that would really benefit from a faucet upgrade. I know it's none of my business and blah, blah, blah, but if you could manage a couple hundred to spend on a more-modern upgrade for something you use many, many times every day could really perk up your kitchen-life.