Your new mailbox will be set up with a username formatted like this: yourname@yourdomain.com and a default password. I recommend that you login to the webmail at http://mail.yourdomain.com and change your password to something you can remember. Then, you can manage your mail through the webmail, OR following the directions in item 2 below, set up your mail on your local computer mail program like Microsoft Outlook. The "cool" thing to remember is that mail sent/received in your local mail program is synced in the webmail and on your cell phone. IMPORTANT NOTE: Your contacts and calendar are NOT synced.
Instructions for setting up your mail in Microsoft Outlook, Apple Mail, Windows Mobile Phone, iPhone, etc can be found through this link. (Your mailbox will already be set up for IMAP, so you can ignore step one in all the directions.) In those instructions where it says to enter your Gmail address, that is actually your yourname@yourdomain.com address. You will use the incoming mail server imap.gmail.com and outgoing mail server smtp.gmail.com as the instructions show. The biggest mistake most people make in the instructions is forgetting to change the mail ports. Make sure to use port 993 for imap.gmail.com and port 465 for smtp.gmail.com.
Your e-mail is being hosted through Google with their "Google Apps" service. The Google Apps service is more than just e-mail hosting. It is also a start page, a calendar, online team website, and online applications. You can set your browser's homepage to http://start.yourdomain.com. You can also collaborate with other yourdomain.com users via a shared calendar at http://calendar.yourdomain.com and create/edit/share documents via http://docs.yourdomain.com. You can set up a "team" website at http://sites.yourdomain.com.
Below are URL addresses you can use to access your mail, calendar, etc should the URL addresses that use your domain not work. Make sure to replace "yourdomain.com" in the URL addresses below with your domain name.
Mail - http://mail.google.com/a/yourdomain.com
Calendar - http://www.google.com/calendar/a/yourdomain.com
Documents - http://docs.google.com/a/yourdomain.com
Start Page - http://partnerpage.google.com/yourdomain.com
Sites - http://sites.google.com/a/yourdomain.com