Uuuuuh im not sure how to start to explain where youre going wrong here. Firstly you didn't take his King, you took his Queen, which is good but does not constitute a win. You put the King in check twice, at NbxC7 and NxC7. You can never take the king, you can only check and checkmate it.
Check before checkmate?

so... you did well... there was NOTHING illegal
and you haven't win the game yet... but you are doing fantastic...

Also, you don't have to say 'check', when one of your pieces is threatening the king. Its polite to do so, but its not a rule,
Okay so I'm new to chess.com and playing chess in general...
I just "won" my first game against my fiance but he says that it wasn't a win because he wasn't checked before I snagged his king... he fell into a trap I laid hehe so we were debating the legality of the move...