To learn to use E-Gold, read the E-Gold FAQ here.
It answers many simple questions right off the bat. Now let’s elaborate on that.

Buying E-Gold

The easiest way to buy e-gold or any e-bullion is with your credit card. I’ve personally tried Able-Gold (which only supports credit-card purchases) and the transaction was flawlessly and prompt. I have no experience with GoldEx but it is a popular and professional company.

Other companies offer deposits through wire transfers, manual bank deposits, or other methods - get a good list here.

Selling E-Gold

To convert your e-gold back into your local currency, any of the independent exchange services on this list would be apt. I have no personal experience with any of those companies, however. Feel free to comment and share information on any exchangers you particularly liked or disliked.

E-Gold Security

E-Gold, encrypted with 128-bit SSL, has several security measures to protect you from having your account hacked and money stolen. The easiest thing to do is use E-Gold’s SRK to input your password. This protects you from keyloggers which may be monitoring your keyboard strokes. Upon logging in, review E-Gold’s Account Sentinel which detects changes in your IP address and browser header, allowing or preventing your login depending on how strict your settings are. There is also a home/work feature which remembers your two common locations for accessing your account.