I am going to introduce myself to him

I am going to introduce myself to him
 

I keep thinking "voy a presentarme a él". However, isn't "him" the indirect object in this sentence, since the introduction is being made to/for him? Then that would be "voy a presentarleme", but that doesn't sound right at all to me

"Con", instead of "a". ;)

Voy a presentarme con él. :)

But doesn't this sentence still require an indirect object pronoun since there's an indirect object (él)?

"Voy a presentarme para/ante él" (it's not an indirect object in Spanish) is the form I would say. Possibly, "presentármele" is correct; but it sounds horrible...

A pleasure.

Voy a presentarme con él
(presentar -hacerse conocer- = introduce <to be seen is not enough, some interaction is required to perform the action, hence "con">)

Voy a presentarme ante él
( presentar -mostrarse en la presencia-= appear before/turn up/show <to be seen is enough, hence "ante">)

Where my confusion comes from is I'm reading the book "correct your spanish blunders" which states: ". Contrary to English usage, the indirect object pronoun must always appear before the conjugated verb in Spanish, even if it is also otherwise named".

So even though "él" is already mentioned, don't we still have to use "Le" somewhere?

There is no indirect object involved. A prepositional phrase completes the verb.

Oh, and by the way, your book is wrong about the indirect object pronoun always having to be present even if it is otherwise named.

I'm not understandimg how el isn't an indirect object...isn't an indirect object who the direct object is directed toward or for? In this case the introduction is direct toward él

The problem here is the verb you're using for being accompanied by an indirect object.

As Julvenzor said, if you must use an indirect object pronoun, the right order of pronouns should be "presentármele"; but this is a formula that is not used for what you want to say.
With the verb "presentar", you use prepositions, instead of pronouns, which also change the meaning of the sentence, like Alec explained.

If you say "voy a presentármele", more than "I'm going to introduce myself to him", it would be more likely understood as "I'm going to show up in front of him" (a possibly annoying attitude).