To remove a file for example 'myfile.txt'; which is already committed and a part of repository, the first step is to 'staging' this file deletion using 'git rm myfile.txt' command. After this command if we use 'git status' it will show message e.g. 'deleted: myfile.txt' . Now as second step to make it permanently we have to commit this staging using 'git commit -m <your message>' command.
Another way is if we remove the file 'myfile.txt' from the working directory manually for example using terminal rm command or using menu as we delete file normally using operating system's GUI. post manual removal the 'git status' command will display the message 'Changes not staged for commit:' and file information like 'deleted: myfile.txt'. To stage these manual changes(we can say same behaviour as working directory changes of add/remove/update files) we have to use -u (recursively update) option with add e.g. 'git add -u'(pre git 2.0 version) or 'git add .'(git 2.0 and above version) command. Then use git commit command to make them permanent.