Firstly, go to World Chat by clicking the area as indicated below
Here we arrive at "WORLD CHAT"
Lets choose one person to add.
At the chatbox provided above, type in that player's alliance code
Double click the text numbers and you will get something like this:
Drag the ends of the code to the side to fully highlight the code
Press and hold the highlighted code, then press copy
Go to the add alliance page by pressing the alliance button at character page
You will arrive here
Press and hold at the box shown, then press paste
You will now see the code pasted in the box
Press request and you are done :)