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It seems to me “take efforts”, “take a great effort” “take the effort to do something”, all three are ok. But I wonder whether you say “take effort” as a set phrase to mean something abstractly, for example:
People always take effort to be a better person, though they may be ignorant of what it means to become a better person.
Something can take effort to accomplish. No one would doubt that it took Einstein some great effort to develop his theory of relativity, even though it is an abstraction of a sort. Something can also take courage, take time, take honesty, take patience, take kindness, etc. In this case, taking means meeting a requirement.
However, the person actually expending this effort is making the effort. One can make an/the effort to be a better person, though this takes courage, honesty, etc. You can also make time to do things. Make is a complicated verb, one meaning meaning of which is to cause (something) to exist or come about; bring about. One makes changes.
edited to add OP's example:
It takes effort to become a better person.
but
People make an effort to be a better person...
You can also say that you put effort into something.
You need to put effort into completing your master's degree.
