In Thunderbird's case alias's are called multiple identities. You can chose an alias when sending by selecting it from the From: drop down list. How to add another identity:
Go to your account settings.
Choose the account to which you wish to add additional identities.
Click the "Manage Identities..." button (on the lower right).
Click the "Add..." button and then add the necessary information for the additional identity for the account.
Repeat as necessary for additional identities.
http://kb.mozillazine.org/Multiple_i...e-mail_account
The details and terminology vary for other email clients, but its a common feature.