Your first stop should be the App Store, to download a copy of Boxcar. After installing the app, create an account by supplying an email address and password.
On the main screen, tap the Add button to create a new service in your Boxcar account. Scroll down the list of options and choose Email Account.
On this screen, you can name the account, and choose options. Boxcar lets you customize your alert sound, and choose whether to display the full message, a more private generic notification, or no text alert at all. If you use a third-party email client, you can also set Boxcar to automatically open a compatible client when you respond to a notification.
Now that your account is set up in Boxcar, it's time to start getting notifications. You'll get an email from Boxcar with a custom email address. Any time mail gets forwarded to that address, Boxcar will ping your device with a notification, based on the preferences you set for that account. But don't worry, Boxcar doesn't store your messages. They just grab the sender and subject to include in your alerts. Everything else about your email will continue to function as normal, including using your regular mail client to read and respond to messages.
You could simply forward all your incoming mail to your Boxcar address, but that would essentially duplicate Mail's existing push notifications. The magic of Boxcar is that you can set up rules to selectively ping your device for certain specific messages.
For example, you could set up Boxcar with your work email address, but only forward messages that come from your company's domain. That way, you'll be instantly alerted to messages from colleagues, but messages from customers or vendors won't bother you when you're away from the office. You can even set a time period for Boxcar to stop notifying you, so your iPad isn't beeping while you're trying to sleep, or so you only get alerts in the evenings when you're out of the office.
Setting up rules will vary depending on your email provider, but the process is generally very simple. In Gmail, for example, go to Settings > Filters > Create a new filter. Enter your filter criteria, and have Gmail forward matching messages to your Boxcar address.
Now, you'll never miss a crucial message. And you can expand Boxcar's notifications by adding additional services. Boxcar supports custom alerts for Twitter and Facebook of course, but you can also create custom notifications for tons of other services like Foursquare and Google Voice. There's even a module to alert you to new iTunes Store sales reports for your iTunes Connect account.