First I believe you have to be a VIP member with a handle.  If so, click Account Manager, then click Edit My Aliases on the left-hand side of the page.  Type in your choice(s) and hit the add alias button.  If your choice is good you'll see it added in the box above where you added it.  If someone else already has that alias, it will be duly noted.
To use an alias you've added, simply hit the down arrow under name when you initiate a post and you'll see the alias which you can click instead of your TER handle.
Easy  huh?

Out of curiosity.......can a moderator tell what account name is behind the alias when someone uses one?? Just curious

Alias' can you be humorous if used for that purpose; however, many people use the to maske their real identity, so they can post things that normally would not.

My advice is that if you have never used an alias, no need to start. If you feel compelled to use one, only use it spariingly, and never to bash or be harsh to anyone.

1. Use of topical humor

2. The creation of a character(literary license) to be used in an informative, fun, innocuously sarcastic, philanthropic etc; as well as topical way.

3. Anonymity for when regional or associational sensitivities may be of concern.

4. Innocuous playing of "devils advocate" in a discussion or debate where one wishes to not be further/future aligned with one faction or the other.

5. Avoidance of suffering political fallout for a comment that may have been misread in a possibly volatile discussion.
(Ain'tcha ever had someone not understand what you were get'n at?)  

6. aliases may be used for posting investigative reports, meet & greet announcements, helpful advice, or other similar types of useful information where the use of a user-name could prove problematic.

7. To 'classify' the content of the posts.
(You can readily surmise the post's cant when you see the alias 'Cynicalman')

8. Concerns in revealing your review history.

9. Ability to contribute where you would otherwise feel embarrassed to speak candidly.

The ONE bad use that constantly has members whining for their banning is the cowardly hiding behind them so one can "flame" without public/political retribution.