“Ça prend du temps”

“Il faut du temps” is closer to “It needs time” and “Il met du temps” is “He puts time” which doesn’t make a lot of sense.

What is the best way to say, “It takes time”?

“Ça prend du temps” is entirely valid and is a literal translation of “it takes times”. It’s the most used.

“Il faut du temps” is closer to “You/It need/s time” meaning that you will be needing time but it can also be substituted for “Ça prend du temps”.

“Il met du temps.” means that “he” is taking/putting time towards something. I have also heard it in the context that somebody is late “Il met du temps à arriver”.

you also see “ça met du temps”, “ça demande du temps”.

“il met du temps” is totally different since it refers to the time a given person is taking, while “ça” is impersonal (and could apply to delays not depending especially of somebody).