Exchange is Microsoft's corporate email, calendar, and contact system, and ActiveSync is their fairly awesome protocol to keep it all updated on all of your devices, including iPhone and iPad. Google licenses ActiveSync for Google Sync, which used to be available for all Gmail accounts but is now restricted to paid Google accounts. No matter whether you use Exchange directly from Microsoft, from Google, or from your company or a third-party service, it's all setup the same way. All you need to know are your credentials.
It's not uncommon for us to email and message people about plans we're making with them. If you pay close attention, iOS seems to know when we do this by underlining certain text. That isn't just to make it stand out more, it's to make it easier for you to add events to your Calendar app.
If you send a lot of emails on your iPhone or iPad that go to different people, you may want to blind copy some users, or all of them for that matter, so they don't see each other's email addresses. Regardless of the reason, if you forget there isn't a need to delete the email and re-enter it in the appropriate field. iOS actually gives you the ability to move them pretty seamlessly.
If you're writing an email on your iPhone, iPod touch, or iPad and you don't have time to finish, or you're simply not sure you're ready to send it yet, you can always save it as a draft and come back to it later. However, it can take a lot of hunting actually find that draft and get back to it! Luckily, iOS contains a gesture shortcut that can make tracking down all your draft emails a lot faster.
As of January 30, 2013, Google will no longer allow new iPhones, iPod touches, iPads, or other devices to be setup using Google Sync (their implementation of Microsoft's excellent ActiveSync protocol). While existing Google Sync setups will keep working, the next time you want to add Gmail to a device, you'll have to use something else -- namely Google's eccentric IMAP service, which works with Apple's Mail app and allows for a unifed inbox with other, non-Gmail accounts, and the Gmail app, which is excellent but is a silo unto itself.
If you no longer need an email account on your iPhone, iPod touch, or iPad, say if you changed schools, jobs, or service providers, you can easily delete. If you're simply going out of town, on vacation, or otherwise off-the-grid and you don't want the distraction or data demands that might go with mail, you can also temporarily turn it off and give yourself a break.
If you come back to your iPhone, iPod touch, or iPad only to find a ton of new emails you really don't want to go through, or if you opened an email by accident but don't want to forget about it later, you can easily mark one or more messages as read or unread right in the built-in Mail app.
If you've got multiple email accounts set up on your iPhone or iPad, the Mail app will automatically reply from whatever account an email was sent to. But what about when you're composing a new email? If you've got one account you use more than others, you can set that as your default account for composing emails. If you ever want to send from another account, you can still do that too.
The iPhone and iPad are great for quickly handling email. However, if something is important, or requires a lengthy reply, or you can only get to it later, or you simply want to keep your inbox close to zero, the iPhone and iPad are also great for quickly sorting and filing your mail into well organized mailboxes.
If you got a lot of email, you might want to start managing it better by filing it away into specific mailboxes. You can have separate mailboxes for certain people, for projects at school or at work, for sorting important messages you want to deal with immediate, from things you want to keep handy to reference later. Best of all, you can create new mailboxes right on your iPhone, iPod touch, and iPad.