What are the essential components of a logical argument?

Answer 1

The proofs themselves
The sequence in which the proofs are presented
the manner and methods use in presenting them

You need sound basic reasons
Quote from a reference work or an accepted authority
If using circumstantial evidence, have a sufficient array of facts
You need an effective summary
A Final appeal to reason
Review the facts and reach the desired conclusion
If this is so, and this is so, then we must conclude this

Answer 2

Ideally, it should be logically consistent and free of logical fallacies.

It should be consistent with reality, observation, and/or experimentation.

It should be grounded in reality, meaning it should be falsifiable.

Any assumptions it relies on should themselves be well-supported, free of logical fallacies, and both self-consistent and consistent with observation/experiments/reality.

This is probably not complete, but it's what I can think of off the top of my head at this late hour. Check out the links below. The first two are different sorts of logical fallacies, while the third is about critical thinking.