You're not stupid. I've had similar troubles with nineteenth century highfalutin political prose. That stuff is genuinely hard for most people to read when we come in cold. I don't know that there's a cure for it except slowing down and reading closely. Eventually you get used to it.

Let's take the first paragraph.

The period for a new election of a citizen to administer the executive government of the United States being not far distant, and the time actually arrived when your thoughts must be employed in designating the person who is to be clothed with that important trust, it appears to me proper, especially as it may conduce to a more distinct expression of the public voice, that I should now apprise you of the resolution I have formed, to decline being considered among the number of those out of whom a choice is to be made.

Never use one word when you can use forty, right? And this is edited down from Hamilton's larger draft from Washington's specs and the speech that Madison wrote for him on the same subject a few years before. It's all written as one sentence. That's possibly grammatically correct, but not fun reading. The modern style is for considerably shorter sentences. Cutting it up more like that, we come to this:

The period for a new election of a citizen to administer the executive government of the United States being not far distant

"A citizen to administer the executive government" is the president. So we can rewrite it as "Presidential election time is coming up."

and the time actually arrived when your thoughts must be employed in designating the person who is to be clothed with that important trust

That important trust is the presidency. You designate a person to clothe in its powers by election. So George is saying here that with the election coming up, it's time to think about how to vote.

That being the case:

it appears to me proper, especially as it may conduce to a more distinct expression of the public voice, that I should now apprise you of the resolution I have formed

Since the people are shopping for a president, Washington wants to help them out. He knows something that they do not, and telling them will help with their decision. That information, of course, is that Washington has made his own decision.

to decline being considered among the number of those out of whom a choice is to be made

And that's the decision. Count George out. He is, as we would say, not a candidate for the presidency of the United States.

It probably takes a skim or two just to part out the paragraphs like this, but the commas are usually good markers. Reading it aloud may also help.