Gmail is not your grandfather's Web-mail. Google very innovative use of newer browser technology to make interaction with their Web services more dynamic. You first notice that things are snappy instead of clunky. Gmail only needs to download the changed part of the next Web page when you access a new message or action. That way, you don't have to download the whole enchilada each time. Things happen quickly when you click on an action or item -- before you forget why you clicked. ;-)
Send an email message to me, with the words "Gmail Invite" in the "Subject". I'll send you a Gmail "invitation" that you can use to open a Gmail account with. You don't need to use a mobile phone for validation if you have an invitation.
It's the large storage capacity that catches most people's attention. Yes, 2,000 MB is nice in itself (almost 3 CDs worth), but the real reason the capacity is there is to make "archiving" all your email feasible. Archiving coupled with "conversations" makes Gmail unique and effective. (Conversations keep related messages linked together.)
The rest of the Gmail package is equally well done. There's a good Bayesian spam filter, "labels" so you can earmark messages to keep them in categories, "conversations" to keep messages and replies grouped together, support for POP and SMTC, and as you'd expect a powerful way to search all your current and archived email.
The original message, replies to the message, and subsequent replies are automagically linked together in "conversations". Say you go back and forth five or six times with someone on a single topic. Gmail links them all together as a conversation in chronological order. When you open any one of them all the rest are right there, ready for you to review if you need to.
You don't delete old Gmail, you archive it. With regular email, when you delete a message to reduce the clutter it's gone forever.
With the Gmail archive, it's not gone, it's just out of sight. If you ever need to find an old message it's easy to retrieve it with the powerful search function. All messages that were in the original conversation are there too. You can search by keywords in the subject, in the message, or by who it's from.
It takes a while to get comfortable with the archive. Start out by tagging your messages with Gmail "labels" before you archive them. They don't totally disappear that way. It's somewhat like folders, but you can tag a message with multiple labels and when you can't seem to find one using the search, you can locate it under the label. Once you have it, you can see better how you could have found it using search.
Gmail has the same limitation that all "Webmail" has -- you only have access your email when you're online. Gmail does not store your messages permanently on your hard drive. You can always save messages, or use Gmail's POP (download with an email client) feature, but that can get tedious if you get a lot of important email.
If you send a message from Gmail to your Gmail address, either directly or through a forwarding service, Gmail will only show the "Sent" copy. The message will never show up in your Inbox. That's important only when you want to test something like an alternate email address that you use to avoid spam.
Firefox is the ideal browser for use with Gmail. Mozilla and Google worked closely during development of Gmail to assure that Firefox and Gmail would work together seamlessly. In addition, Firefox extensions can be used to further enhance Gmail convenience and functionality.
You can find messages more effectively, even those in "Trash" or "Spam" by using search options. Click the "Show search options" link up by the search buttons. You will then see several options. One that is not so obvious is searching through spam and trash. Just click the down arrow by the box for "Search:" and select "All & Spam & Trash", not "All Mail", which just searches through the mail in your Inbox and Archive.
Putting a label on a message in Gmail is like putting a message in a folder in any other email service or client. However, Gmail lets you put one, two or more labels on a message. That's somewhat like making copies for each folder you want to be able to find the message in.
For example, you might receive a message that contains driving directions for an appointment, and a schedule of all events for the year. You could put both an "appointments" label and an "events" label on the message. Later, you could find the driving directions by looking in appointments, or see the schedule by looking under events. Simple really.
"Getting Started with Gmail": http://gmail.google.com/gmail/help/start.html
How to import your address book to Gmail: http://gmail.google.com/support/bin/answer.py?ctx=gmail&hl=en&answer=8301
"How to Use Gmail": http://www.gmailusers.com/tutorials.htm
The mother lode of Gmail tips: http://g04.com/html/backend.php