Most login-based websites only allow one login session to be accessed at a time, due to the way browsers work. This can be a problem if you have multiple accounts.
Some people just open up their second-rated browser (e.g. IE), and run their second account on that. I don’t like doing this as you lose the capabilities of your prefered browser (Firefox) in that instance. Also, what about if you have 3 accounts? Install Opera/Safari?
There are two ways of running multiple sessions in Firefox.
Session Manager plugin
The first being using the Session Manager plugin. This lets you save the current session, and then lets you change the session (e.g. logging into another account), and switch between the two. This can be awkward if you want to access both accounts simultaneously.
Multiple Firefox Profiles
An alternative is to run another Firefox profile as a separate process. The problem is by default Firefox only lets you open up one process at a time. You need to force it to open a new one.
To do this you can just run the command/create a shortcut:
firefox -p -no-remote
This will open up a new Firefox process which you can then create/load another Firefox profile in, all whilst running the other Firefox process.