First, create a table with a field for days and a field for today's link, both of which are initially empty. Everytime your page is loaded, check the database to see if today's date has already been entered.
If it has not, generate a random number and use modulus to get an index number within your table of links. Grab the link stored at that index. Then, insert into your days/todays_link table today's date and that random link. Then use that info for displaying on the sccreen.
If that date has already been inserted into the table, just grab the info from there and send it to the browser.
There are probably better ways of doing it, but that's what popped into my head first. You should be able to handle the code for that.
EDIT: Ha! I must be faster next time. planetsim beat me to the punch, but at least our ideas are similar!