The "Brazilian method" is really just a trick to install games as if they were legit, whether or not your "backup" was dumped by yourself or not. In order to do this, you will need an external HDD to install the games to, OR enough space on your system's internal memory. You will also need WUP installer (or another similar application) on your sd card. Once you have these things ready, you run the browser exploit which will boot you into homebrew launcher. Now homebrew launcher should recognize the apps you have on your SD card, and you want to run WUP Installer. Install the game to the hard drive of your choice, and you are done. Once the game has been installed, you can launch it just like any other legit disc or eShop game you have; there is no need to re-run the browser exploit.
Loadiine is different in that it hijacks another app (default: Mii Maker) and allows you to boot unencrypted game files. Note that this means the game files for Loadiine are incompatible with the Brazilian method and vice-versa; if you downloaded a game from the internet, take note of which type of files you are getting. Loadiine has a variety of compatibility differences, but most notable is that you cannot connect to internet services for games launched through Loadiine. Your save files will also be stored separately on your SD Card as opposed to using the Wii U's built-in save management, and you cannot install games to an HDD or internal memory with Loadiine. To run Loadiine games, you must run the web exploit and then launch Loadiine from the Homebrew Launcher.
RedNAND is a bit more complicated and potentially more dangerous. While information has been shared publicly, most of it is not really intended for your standard end-user. Therefore, this should be your last option; only resort to it if Loadiine and the ticket trick (Brazilian method) do not give you what you want. RedNAND allows you to boot basically anything. You will still have to go through the web exploit and boot up RedNAND each time you boot the system, if I understand correctly. (RedNAND installed games may show up on SysNAND, but they will not run from there.) There is a trick which allows you to boot directly into basically anything, including RedNAND - it has been referred to as "coldboothax". HOWEVER, this is where the risk comes in. While RedNAND itself poses practically no risk, it is quite easy to brick your system trying to install coldboothax if you don't know what you're doing. I would recommend waiting a while until some of these things are more thoroughly documented and released in a more user-friendly fashion that is safer for everyone.
I tried to open one game that I downloaded Captain Toad, using loadiine but I got a black screen for some minutes the I restarted. Does this game not work with loadiine or did I something wrong.
There is a Loadiine compatibility list here:
https://wiki.gbatemp.net/wiki/Loadiine_compatibility_list
Generally speaking, most popular games work fine and Captain Toad: Treasure Tracker should work. My guess is that your dump was corrupted or encrypted, which is not suitable for Loadiine.