If you would have notice most of the web service like Facebook and Twitter allow only one user login from a given browser at any given time. For the people who need to monitor two of such account at the same time have to use two browsers to do their work.
Now here is the trick to open more than one account in the same service using Firefox and Chrome.

For Firefox Users

1. Download and Install the Multifox Plugin. Allow any application request in the installation. Multifoxis an extension that allows Firefox to connect to websites using different user names. Simultaneously.
2. Once the Plugin in installed successfully restart your Firefox.
3. Now right click any where on the Tab bar and select “Open in a New Identity Profile”.
4. Selecting this option will open a new window using which you can login to same service with another username.

If you don’t want to switch windows you can drag and drop the tab in the existing windows.

For Chrome Users

Google thinks so much for their users. Unlike Firefox fans you guys don’t need to install any plugin for the trick. Just initiate incognito tabs using Ctrl+Shift+N and open same service with two different account