mkdir makes a folder. mkdir -p makes a whole path in one go and doesn't complain if it's already there: mkdir -p projects/duck/notes. touch makes an empty file (or updates the date on one that exists).
cp copies and mv moves. Both take the source first and the destination second. If the destination is a folder, the file goes inside it with the same name; otherwise it gets the new name. That's also how you rename: mv old.txt new.txt.
$ mkdir backup
$ cp notes.txt backup/
$ mv notes.txt ideas.txt
$ ls
backup ideas.txt
$ ls backup
notes.txt
To copy a folder and everything in it, add -r (recursive): cp -r photos photos-old. mv moves folders without it.
rm deletes files. There's no bin and no undo: the file is gone. rm -r deletes a folder and everything inside, and rmdir deletes a folder only if it's empty, which makes it the safer choice. Add -i to have rm ask before each file.
Be careful with names that have spaces. rm my notes.txt tries to delete two files, my and notes.txt. Put the name in quotes: rm "my notes.txt".