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 <kbd>⌥</kbd> 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.