Your new iPad is a great way to stay organized and focused on the activities and events that matter to you most. The built in Calendar app has a lot of great features and tools to help you create, edit, manage, and share your schedule, including event invitations.
Before you can start creating and accepting proper event invitations you need to have set up either a free Apple iCloud account (@me.com address), or a Microsoft Exchange ActiveSync account (including a Gmail account set up as Exchange).
iCloud allows you to share an event when you create it, or share it later if you choose to.
While users with other types of accounts will receive your invites, they won't be able to accept them into their Calendar and see your changes to events if they aren't using iCloud as well.
If someone has sent you an event invite, you can accept them straight from your iPad with just a few taps. Depending on your settings, you might get a popup notification or email alerting you when a new invitation comes in. Your Calendar app icon will also be badged with a number representing any outstanding event invitations (similar to how Mail shows you the number of unread email messages.)
To accept an invitation: