Once you have your new iPad all set up, you're going to want to get your contacts sorted out so you can email, iMessage, FaceTime, Skype, and otherwise stay in touch with the people that matter the most to you.
When you set up a cloud-based email account, be it iCloud, Gmail, Hotmail, Exchange, etc. all your contacts will be synced over as well. Everything that you have online and on your other devices, like your smartphone, or on the Web, will just show up, and will stay in sync no matter where you make changes.
That's all there is to it. Contacts will automatically integrate with Mail and other default apps so you don't have to type in email addresses or phone numbers. Just type the contact name and it should pull just exactly the right information, as long as it's in your contacts. And if you're synced with iCloud, ActiveSync, or any other type of cloud service for contacts, your changes will also be reflected on any other iPad, iPhone, or iPod touch you have set up as well.