Org mode uses the standard Emacs minibuffer completion mechanism for tags: whenever a tag is expected (e.g. at the
C-c a m prompt), you can type
TAB to get a completion list. You can click on a completion to choose it (or, without a mouse, switch to the completion buffer, navigate to the completion of interest and press
RET); or you can narrow down the selection by typing a letter or two and pressing another
TAB: when you have reduced the choices to just one, type
RET to choose it. E.g. if I say
C-c a m and type
TAB at the matching prompt, I might get a completion buffer with many tags:
drill emacs export fedora firewalld git html latex linux
nfs noexport org pacc project python rh selinux ssh
e TAB reduces the list to two:
emacs export, and typing
m TAB completes it to just
emacs at which point I type
RET and I am done: the tag
emacs is selected.
At a more advanced level, there are ways to influence what tags are added to the completion list: by default, it's all the tags in the file (e.g. when you try to insert a tag on a headline), or all the tags in all the agenda files (that's what
C-c a m uses); but you can use the variables
org-tag-persisten-alist and you can also use in-buffer settings to modify the completion list. You can find the gory details here or, better, just say
C-h i g (org)Setting tags to your emacs (that invokes the Info system in emacs - learning to use the Info system is highly recommended: you can use emacs to tell you (almost) all about emacs). Although I mention this for completeneess, you should probably not worry about it now. After you get comfortable with standard completion, you might want to come back and reread this paragraph.
The standard Emacs minibuffer completion mechanism is described here but, as above, you can also use Info to get to the same information inside your emacs:
C-h i g (emacs)Completion - and BTW, you can use completion to get to the right place: say
C-h i g (em TAB )Compl TAB and you don't have to type the whole thing (or even remember it). Completion is powerful!
In the future, you might want to investigate some other completion mechanisms that are available (John Kitchin mentions helm and ivy in his answer), but I would recommend that you leave them for later: you can spend years working with Emacs without feeling the need for any of these additional mechanisms.