To type them easily you'll usually need composition (sometimes called chording) support. Some Linux (and other Unix) distributions still have this built in by default, though last time I used Linux for much desktop use it seemed to be fading from common availability, otherwise you'll have to hunt for another method. On Windows I use http://wincompose.info/ (here [atlgr][^][1] produces “¹”, for instance, in the default settings) which is useful for a number of other things (I first started using it for accented characters like á on a UK keyboard). If you have a keyboard with programmable function keys then you could use its customisation tool to map some of them to produce the super-script (or sub-script, or other) characters you commonly want.
For less convenient typing, use your OS's Character Map or similar tool.
On Android, unless you have a different keyboard in use which doesn't support this of course, long press on the number on the touch keyboard gives superscripts as an option.