"Glauben Sie mir einfach."
"Sie" is always capitalized when you use it for formal "you". I assume you are talking about the missing "you" in the English sentence. The sentence is in the imperative mood as it is a command. In a lot of languages when you use an imperative sentence you leave out the subject (as is done in the English sentence) and you might use a different verb form. However, German doesn't have a true imperative for the formal "you" which means that you use both the subject Sie and its corresponding verb form. For the informal "you" you would say "Glaub mir einfach" (different from "glaubst") and for the plural "you" it's "Glaubt mir einfach".
I'm confused. You say that Sie is necessary in the German imperative form, but then in the two examples you leave it out. Is it (or the other two second person pronouns) optional or mandatory?
I.e., is it Glaub du mir einfach, Glaubt sie mir einfach, Glauben Sie mir einfach, or can/should the du/sie/Sie be dropped?
No, the Sie indicates the formal imperative mood. If you want to be informal. you can omit the Sie, but you need to use the stem of the verb instead. So you would say to a friend, "Glaub(e) mir einfach". The e is optional. There are two more forms for informal you-plural, "Glaubt mir einfach", and for first person plural, "Glauben wir mir einfach", which translates to "Let's believe in me". http://www.dartmouth.edu/~german/Grammatik/Imperative/Imperativ.html explains it fairly well