You can buy for about five dollars, a sprayer that will replace aerator on your faucet. No tools are required to make the change. Your local hardware store should have the sprayers.

i just had one of the building handymen replace the existing faucet with a new but midrange faucet with a pull out spray head. it cost about $100. i kept the old faucet and will replace it when i leave. i also replaced the old light switches with lutron radio control dimmers. i will just put the old ones back on before i leave

I installed a $3 pivoting aerator nozzle from the grocery store on a lark and it actually works great. cheap and easy to install. And your landlord wont freak.

Remember those rubber ones that slip over the faucet and have a switch so you can have a stream or a spray?

You can also get a longer hose with a shower spray on it at the mega mart. They are usually for tubs, but you could keep it around for filling large pots or mop buckets.

Lovely commenters, you have given the OP 3 choices:

1. aerater attached to the tap
2. rubber hose sprayer attached to the tap
3. buy a new faucet with sprayer and replace old one when you leave.

Bravo, commenters!

Britta make a water filter attachment that also gives you a spray option.

I think you probably could get away with switching out the faucet and replacing the old one when you are done. I'm sure it comes in kit form.

One of the problems with the add ons to a faucet is that the faucet is probably low clearance already. Once you add an inch or so to the bottom - the screw on sprayers - you can't even wash a bowl underneath. I've been thinking about a replace with new (now)/replace with old (when I leave) myself.