It's kind of messy. The emulators exist for android (including Citron for the Switch, which works great) but they need firmware files and stuff on first start. Some machines also encrypt games and you need additional or specific file formats for them, e.g. the ps vita.

The switch for example needs an unlock file to start with and some website has it but I forgot the name.

If you look on reddit there's usually resources but it does require some research. For the PS Vita for example NoPayStation is the best source, it has the game files AND the accompanying .work file that you also need.

You can either download everything on the tablet directly or connect it to your computer with a USB cable and transfer the files. For the emulators install the .apk files. For games I usually create a folder in the root folder on my phone (so like no subfolders or anything, don't overcomplicate it) named after the emulator and I drop my games in there. Citron will ask you so select the folder, I do, and it just reads whatever's in there. Other emulators like Vita 3k need you to install games individually but I still keep them in a "Vita 3k" folder so I know where to look for them.