Note: This post was written using iOS 6, the look of some icons might have changed and few features may have been added or moved in iOS 7 but for the most part it is the same.
Really your iPad is suppose to help you be productive, it can help you do that by allowing you instant access to such basic productivity tools as your email, your calendar, and your contacts. Now you could just go through the iPad's safari web browser to whatever your preferred productivity suite's website is and access them that way, but it is far more productive to use the iPad's stock apps(mail, calendar, contacts), or another app of your choice from the app store.
I prefer to use apple's stock apps, I have tried other apps, especially calendar apps, and nothing seems to work as well for me as the ones that just come with the device. Some people do not like the interfaces of these apps and so they choose to go with a different option, some email providers such as gmail also have dedicated apps for the iPad. Regardless of what option you go with you are going to need to set up your account(s) from the settings page.
We will be dealing with the two options inside the red box today. The most simple option by far is to just use or set up an iCloud account. Since iCloud and the iPad are apple products working together, this option seems to work well (although not always flawlessly). It is an easy process, just click on the iCloud tab and enter your apple iTunes account information (if you do not have an iTunes account now would be a good time to set one up since you will need one to get any apps on your iPad) it will then either log you into your existing iCloud account, or walk you through the process of creating one.
After logging in you will be able to toggle on and off which services you would like synced through that account.
Now if you are a mac user, or if you have decided to forgo a computer completely and just use an iPad, than you could feasibly use only iCloud and be fine. But most people have a work email account, or another calendar account, etc that they would like synced with their iPad. This can be done through the Mail, Contacts, Calendars tab. Click the add an account button, shown in the orange box above. You will then see these options, select your email server by clicking on it. If your server is not listed select "other."
Then you simply enter in you email address and password for that account, they will also ask you to give the account a name and a description but that is only necessary if you are going to have multiple email accounts on your iPad. The iPad will check it and once verified it will as, you what you would like to sync with that account (email, contacts, or calendars). Turn on the feature you desire and poof! your iPad will sync them over and they will appear in the standard Mail, Contacts, and Calendar apps. The account will now appear under "accounts" and you can change the settings for it or delete it at any time by clicking on it.
Fantastic, if you have an questions just put them in the comments below and don't forget to share if you know someone who need a little help.
That's all for now, and remember, live better.