
At the top right, you should see your account name, as usual. Sign out of any currently logged-in accounts.
If you're used to just clicking and moving on, you may want to read these, as they're pretty informative. Click On, then tick the boxes next to the info statements that follow it.
Head over to the Google Accounts Multiple Sessions page. Log in to Google using any service and account you'd like (Gmail, Google Calendar, Google Docs, etc). Google has relented, and now lets us keep up to 10 accounts signed in at the same time on one browser. There are plenty of reasons to keep multiple Gmail accounts, but until quite recently, our only option to keep them open simultaneously was to keep them in separate browsers, which is a massive pain and too resource-intensive for many users. Maybe we just like to confuse our friends. Maybe we want to maintain multiple online identities (for perfectly legitimate reasons). Maybe we want to keep our work and social lives separate. They're still rolling it out, but it's easy to opt in to the service. Editors' note, August 14, 2012: Sharon Vaknin just posted about Google's Account Chooser update that makes this even easier.