As you can see from the video, the word 'out' is a very versatile word with many uses in both a social and professional context. While that can make it seem complicated, many of the variations are actually grouped together under a few meanings.
Go out, eat out, out on the town - leave your house or go outdoors, often to socialize.
Outdo, outrun, outsmart, outwit - go beyond or exceed somebody at something.
Back out, break out, got out of, bail somebody out - avoid something or free yourself from something or the responsibility of doing something.
Out of cash, run out of, out of fashion, out of date, out of time, on the way out - no longer viable or have no more of something.
Hand out, give out - distribute something freely.
Find out - discover something by chance or through effort.
Fill out, write out - provide what is necessary to complete a document or form.