your visa is a sticker that's IN your passport. you can get it via the mail (be sure you've got plenty of time for it to be mailed back to you) or if you live close enough and can make the trip, you can get it in person from the consulate of the country your visiting.
you can get a visa number yourself, like a vistor visa. if you'll already have a job when you get to korea, the visa will be an E-2 visa issued by your school. the visa will state your length of stay and who your employer is. this means that your employer is the only one you can work for.
if you plan on travelling (like to japan for a weekend or something), perhaps ask your school for assistance b/c then you will need a multiple entry visa. i dont think the procedure is much different but the cost is much more. with out this type of visa, you are not to leave the country.
my job emailed me my visa number and i drove to the korean consulate in los angeles to get the visa. i filled out some paperwork and gave them two passport sized photos. The visa was ready to pick up the following business day.
i had more to write before b/c i had a nice little drive to LA, but now im bored. so anyway this is all the basic info here. ok bye.