If you can't find an auger to use, take a pipe wrench and try to clean out the trap below the drain. Use a wet/dry vac to slurp the water out of the sink, but be sure to also have a bucket down below.
Every plumber I have ever spoken to says to NOT use the drain cleaner chemicals. They can clear a mild clog, but they do it by gluing the gunk to the sides of the pipe which makes it far more likely to clog in the future. They are also very hard on the pipes. The auger is teh best way to approach a clog. Taking the drain apart and cleaning the pipes or replacing them is also a good solution.
I have a drain to clean out in my bathroom. Somehow the sink stopper is fastened into place and I can't get the auger thing in. It gets huge hair clogs.
Walmart has a $2 disposable tool that is made out of white plastic. It has teeth sticking out either side and it is made to go into drains like mine. It grabs the hair and other ick that clogs the pipe. You just thread it down in, wiggle in a bit and then yank it out - usually with a bunch if icky goo with it. It has been a good solution several times for us.
). He bought an auger. He ran the auger from the sink to the basement for about twenty feet. It's draining, but still a lot slower than before he started yesterday. He says he will auger out to the main line tomorrow. 
