How do I send a group email on my iPad Air? I'm having trouble sending email to a group from my iPad (with the email app that came with the iPad).

The groups are there under my contact groups. I open a new email, click on the "to" field, and then click the "+" button, click "groups", click on the group that I want so that there is a check mark next to it, press "done", click back to the email, and then the "to" field is still empty.

What am I doing wrong?
The tick mark doesn't mean that you've added them to the To field — it just means that you've narrowed down the list of contacts to that group.

When you tap the + button to add to the To field, by default it shows All Contacts. Pressing Groups lets you narrow down this list to that specific group, but you still need to select the people that you want to send the email to. Tap them in the list (and select their email if necessary) to add them to the To field.