Sorting into categories needs you to first make the category that you wish to sort messages into. This option is at the upper left when you go to your inbox. There is a small option called "add category". Click it and proceed!
From there, you can select the tickbox next to the desired conversations that you wish to move. When you have them selected, a new menu bar will appear at the bottom of the screen with a dropdown menu that says "choose action". Select "move conversations" from the list of choices and hit "GO".
From there, it will ask you to select the destination category for your conversations. The default is "all conversations" but you can change it to the category that you just created and hit "MOVE". Since all conversations appear in "all conversations" make sure that you don't select any conversations that you have already moved or it will tell you that there has been an error.
If you're running into issues starting new conversations, try following the first step in the above process to create a category.
At the right side of your inbox just above the name and date of who sent you conversations, you should see a little option called "filters". Select it and it will open a dropdown menu with some filtering options. You can filter it by who started the conversation or who you sent the conversation to. You can also star conversations and sort by starred conversations in the filters!
Starring conversations works much like selecting them to move except instead of choosing "move conversations" on the menu that appears at the bottom of the screen, you will choose "star conversations".
The search function is just a search but finding it can be hard if you don't know where to look. To locate conversation search, first go to your inbox. From there, the option is just below the standard menu that sits at the top of the page, approximately underneath the "characters" dropdown.