You will start on the COTC library home page: http://library.cotc.edu/ On the right hand side of the screen, you should see a link that reads: Research Databases List. When you reach the list of databases, select the name of the database you want to use. You can then sign in with your name-# and password, just as you sign into MyCOTC.
There are also step-by-step instructions (with screenshots) available here: http://osu.campusguides.com/cotc_off_campus