I think the key is that you must have a shared secret in advance, which is probably something you won't have in most cases unless you're building a point-to-point encryption.

I'm afraid I don't have such an article, and I'm not an expert (just a dog right) but the article that explained Diffie Hellman in a way that made me feel like I was understanding it, you each get a paint color, and you have a pre-negotiated shared secret color. You mix the paint colors to send signals and you know what the colors look like when they are blended with the secret, because you've seen them before.

What's missing from this to make it safe from replay attacks? (It's obvious that if this is the whole setup, if you could observe the color transmitted, you could simply pass the color again if you wanted it to appear that the message was transmitted a second time.)

The answer I think, is a Nonce or IV (Initialization Vector.) I'm not particularly clear on how a nonce is different than an IV or if you would only ever use one or the other, or if you might use both in certain cases, or in all cases...