Learn Dutch: Vorm de klei zoals ik het uitleg. - Shape the clay as I explain it.

The word zoals (as / like) acts as a subordinating conjunction here. That means it introduces a dependent clause, which forces the conjugated verb (uitleg) to move to the end of that clause.

Isn't uitleggen (to explain) a separable verb? Why isn't it split up into leg... uit?

You are right, it is a separable verb! In a normal main clause, you would say ik leg het uit. However, because zoals sends the verb to the end of the subclause, the two parts of the separable verb get pushed together again at the very end to form uitleg.

Why is the first verb just Vorm without any extra endings?

Vorm is the imperative (command) form of the verb vormen (to shape or form). In Dutch, the imperative is simply the stem of the verb, regardless of whether you are telling one person or multiple people what to do.

Could I translate zoals as "the way" in this context?

Yes! While zoals literally translates to "as" or "like", translating this sentence as "Shape the clay the way I explain it" is a very natural way to capture the meaning of a conjunction of manner.