Learn German: Wir laden die Familie ein. - We are inviting the family.

This is because einladen (to invite) is a separable verb. In a standard main clause, the core part of the verb (laden) takes the second position, and the prefix (ein) is chopped off and pushed to the very end of the sentence.

How is the verb einladen conjugated for wir?

For wir (we), the main part of the verb just keeps its standard ending, making it laden. Together with the prefix, we get wir laden ... ein. (Note: If you were saying he/she/it invites, the vowel changes to an umlaut: er lädt ... ein).

If I want to add a word like heute (today), does ein still stay at the end?

Yes! The prefix ein acts like a wall at the very end of the sentence. Almost any extra details you add will go between the main verb and the prefix. For example: Wir laden heute die Familie ein.

Is die Familie in the accusative case here?

Yes, it is the direct object (the people receiving the action of being invited). Because Familie is a feminine noun, the word for the stays die, which looks exactly the same as it does in the nominative (subject) case.