What is 「好き」 And 「好きます」 In english, And how do you use these in japanese?
Ive seen both of these used in japanese before. I think they mean to like but then i went on google and searched "英語で「好きます」" whenever i did that i got a result for a japanese website that showed japanese sentences that used that word and english equivelents to that sentence. However the sentences sometimes had like and love in them and some used favorite in the translation.

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About the meanings:
好き means "to be fond of" or "like". It can mean favorite as well, especially if it is eg in a comparison used together with 一番 (いちばん) -> most that I like = favorite. Otherwise it can mean favorite if you use it as na-adjective. Depends a bit on the context.
and about that it can mean love: Japanese (as far as I know) don't really say "I love you" literally so smth like 愛してる or so, but rather 好き or even more 大好き. That's ehy you should be cautious when saying 好き in the context of a person. Then it might be thought that you love that certain person.

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好きます　is wrong Japanese. I've never heard it.

You can say 好き or 好きです. 
好きです is more polite.