I'm not sure I understand the problem. You just point your browser to
groups.google.com. There's no need to sign out of anything.
A link to Google Groups can also be found by clicking the "More" link in the Google Menu at the top of the screen, choosing "Even More", and scrolling down to the "Social" section.
If you want to create a link for yourself right in Gmail for your convenience, enable the "Quick Links" Gmail lab.
Adds a box to the left column that gives you 1-click access to any bookmarkable URL in Gmail. You can use it for saving frequent searches, important individual messages, and more.
(Note, however, that this is an experimental feature and may be removed at any time.)