I think it's appropriate to think of like as a preposition, but grammar girl's advice for recognizing a conjunction is a too quick and too dirty. As has several senses, and is only a conjunction in some. You are probably best off simply learning all of the main constructions that have as in them, and abandon any hopes of pinning down a "part of speech" for the word itself.
Consider buying Huddleston and Pullum's Student's Introduction to English grammar, which is close to the same price for clean, slow advice.
A conjunction is a word that joins two elements together. For example, and in the following sentence joins clauses C1 and C2 together.
[Thomas ran to the store]C1 and [Carmen followed him]C2
As is a subordinating conjunction, which means that the clause that follows it depends on (or is syntactically part of) the clause that it is joined to. In the following example, that joins the matrix clause (C1) and its subordinate clause (C2).
[Thomas said that [I'd never learn to read]C2 ]C1.
But conjunctions can also join together elements other than claues. In the following, the conjunction but joins two verb phrases (V1 and V2).
Thomas [was running to the store]V1 but [slipped and fell]V2.
Note that grammar girl's advice will help you to correctly diagnose but as a conjunction when two verb phrases are joined by it, but is bad advice when looking at conjoined clauses or noun phrases, or prepositional phrases...
As can have different properties when used in different constructions. It can introduce a standard of comparison, in which case it acts first a special word introducing an adjectival phrase, and second as a preposition (and not a conjunction in either case).
[Thomas can run as fast [as a wallaby]].
It can serve as a subordinating conjunction, introducing a matrix event. Note here it joins two clauses, and so grammar girl's advice will not help you to realize that it's a conjunction.
[Thomas loads his gun [as Carmen looks on]].
Here's a case where as does precede a verb phrase (an as many/much... as construction):
As many chickens were killed that day as [passed through the gate].