"Ones" is the plural of "one".
Example: Are those the ones you are looking for?
"Ones" is also the possessive form of "one" when "one" is used as a pronoun. There is no apostrophe, similar to "his".
Example: One should mind ones own business.
"One's" is a contraction of "one" and "is", or "one" and "has".
Examples: One's less than two. One's been less then two forever.
If one is used as a proper noun or a noun, then "One's" would be the possessive for the proper noun, and one's would be the possessive for the noun.
Examples: "Number One's skills are better than Number Two's skills" or something like that. I can't think of a great example of a sentence.
Two's value is greater than one's value. (Talking about numbers with the numbers being nouns.)