I can't find a tutorial on how to use it, what to download, etc.
The easiest way to get started is by using the public horizon that is hosted by stellar.org (horizon.stellar.org). Horizon is just an HTTP api that is layered on top of stellar-core (with a few extra bells and whistles) -- so you could make your http requests directly to it like the Stellar Laboratory does.
However, you're probably better off using one of the supported Stellar SDKs -- pick one of them in a language that you're comfortable with.
Start with https://www.stellar.org/developers/guides/get-started/index.html to get a big picture of how the different pieces fit in, then move to the next step that shows you some actual code samples (https://www.stellar.org/developers/guides/get-started/create-account.html).
The Stellar developers site has a lot of other helpful articles on it. I encourage you to read through it, especially the Guides and Reference & SDKs sections.