If you can't work the shutoffs on the water lines under the sink, your only choice is to contact your condo maintenance people. They need to have some way to shut the water off to your unit when they make repairs. They can tell you if there are some more valves in another area that you can access, or they may have a maintenance closet somewhere and can turn the water off for you so you can make the repair.
Sometimes you can turn a sticky valve by using a large set of channel-lock pliers or similar type on the knob so you can get leverage. They look like this if you're not familiar with the type:
If it's been a while since the valves have been used, they often don't want to move without help. Once free, they may work fine, but sometimes it's a good idea to replace the shutoff valves as part of the new faucet installation. They're not expensive and you'll know they will work if you need to shut them off in the future. Get "ball-valve stops" which make a positive shutoff. Stops that use a rubber washer can sometimes let water trickle through (or more than trickle!) when shut off. Depending on the kind of valves currently installed and the type of pipes supplying your water, you might want the condo maintenance people to do the replacement. But if 1/2-inch copper pipe is what you have and there's a couple of inches between where the pipe comes through the cabinet back or bottom and the current valves, you can just cut them off with a tubing cutter. Then you can replace them with valves that just slide over the pipe and are fastened by tightening down a compression fitting (tightening a nut, in other words).
You should also plan to use new supply lines from the shutoffs to the faucet. Again, they're cheap and the old ones can sometimes leak when you try reconnecting them. Corrosion and mineral build-up from hard water can lead to poor sealing. The current ones may also be clogged with minerals, and new ones will give your new faucet full flow.
Once you've got that problem of turning off the water supply solved, it's usually not too difficult to change the faucet. Make sure you have a basin wrench on hand; on many faucets it's impossible to reach the supply connections with any other kind. The box from the new faucet may tell you if can get away without one.
Good luck with the project, and thanks for using Fixya!