Well i have explored number of ways to open youtube as an anonymous user and as a user signing in their account.
I will be explaining the ways according to users skill level.
1. Beginners (proxy site)
2. Intermediate-expert (proxy tool)
If you want to add this as an "ADD-ON" in mozilla firefox, you will be required to drag and drop wj-button file to firefox toolbar.
Using a vpn software is another option but for that you be will required to purchase it.