How to Use Skype Without Downloadingby Vanessa Padgalskas
As long as you have a Skype account, you can log into Skype on any computer with Internet access without having to download Skype. Skype is free to use when calling from computer to computer, and includes video chat, voice chat and instant messaging.
Go to the Skype website (see Resources).
Click on "Sign In" in the upper right corner of Skype's homepage.
Enter your Skype account username and password into their respective blanks, then click "Sign Me In."
Click on the name you want to call just like you would do when Skype is downloaded to a computer.