I've checked Nexus Mods and in-game there is a mods section (yes, there are mods), but as someone who really hasn't modded. How do I mod the game? Where do I put the mods? Etc... (Obviously I know how to download the mods)
Windows & Mac (Both will help)

Thanks in advance.

I dont think they have released the Dev tools for this one yet.

Here is a good guide on modding by Spud Dastardly

http://steamcommunity.com/sharedfiles/filedetails/?id=772694134

With Nexus mods, download the mod in question, then unzip the file into the folder:

Documents > Master of Orion > Mods

I'd recommend keeping each in their own folder for ease of management.

Steam mods will largely require you to have the game on Steam, which they don't mention as you're developing the mod, and they don't mention when you're uploading the mod, which is a tad manipulative. If there is a way by which you can download the mod files manually, I'd love to know myself.

I've done this but the mods ('UnofficialCodePatch' and '5X - The Ultimate Balance Mod') don't show when I go to the Mods section of the starting menu in the game. What have I done wrong?

I just want a mod where ships in orbit, can be selected from the production screen for an upgrade to any variant of that ship's class.