Even without Admin privileges, you can use the Finder's Go menu to access the library folder. Click on Go, then choose Go to folder... near the bottom of the dropdown menu.
In the resulting dialog box, type
~/Library
and hit Return.
EDIT: Alternatively click Go press ⌥ and click Library as it will show up on the key-press.
Your Library folder will open in the active Finder window, or in a new window if one isn't already open.