1. Something exists. (Premise)
2. If there were more than one thing, then they would either differ by being or by non-being. (Premise)
3. They cannot differ by being, since being is what makes them identical. (Premise)
4. They cannot differ by non-being, since to differ by non-being is to differ by nothing, and to differ by nothing is to not differ at all. (Premise)
5. Therefore, only one thing exists. (From 1 - 4)
The argument is logically valid, but it's premise (2) that is demonstrably false. Although there have been many different attempts to circumvent this premise, I'm persuaded that Aristotle provides the best alternative. While things are identical in their being/actuality (that-ness), they differ by their various essences (what-ness) and their varying degrees of potentialities. Only Aristotle's Unmoved Mover is Pure Actuality, whereas other things (while participating in the actuality of the Unmoved Mover) are distinct from the Unmoved Mover due to their potentialities. For example, an acorn is merely a type of seed in actuality, but it is an oak tree in potentiality.
I'm not going to defend the First Way in this post, with the exception of premise (1): Evident to the senses is change. Alternatively, (1) can be stated as: Things change.
Now, why is this premise metaphysically certain? Aristotle provides the following criticism of Parmenides's argument. Coming to the realization that all change and all distinction is illusory itself constitutes a change, making the argument of Parmenides literally self-defeating. We can know with certainty that things change, or at the very least, that things have the potentiality to change.