Beginner to chess, need tips or guidance on how I could have mated opponent?

10. f3 Qxd4+! 11. Qxd4 Nxd4 12. fxg4 Nxe4 (Very precise for a 670. I like this.)

13. c3 Nc2?? (14. Rc1 and the knight is trapped. 13... Nxb5 (14. c4 Bxb2? 15. Rb1) (14. a4 Nxc3!! 15. bxc3 Bxc3 where you are three pawns up with four potential passers to their none.)

14. Bxc7?? Nxa1 15. Bf4! (The knight cannot be saved. The only way out (Na1-c2-e3) is now blocked.)

One thing you need to work on is too look for pieces that are not protected.

Correction: 15... Nxc3!! 16. bxc3 Bxc3 and you are up an exchange and two pawns, with the army of passers I mentioned before.

Advances like ...e5 are coming next.

16. Bc7 Nc2? (Loses the exchange for nothing. 16... Rac8 17. Bf4 e5 is refuted by 18. Be3 where the knight is not getting out.)

my best advice is to practice with the tactics trainer, watch a bunch of videos/tutorials about the openings and strategies that you favor, and really learn how to develop a plan of either attack/defense.  

17. Bxd8 Rxd8 18. Bd3?? Rxd3 19. Rf4 Rd1+ (Great! 20. Rf1 is forced, after which you have 20... Rxf1+! 21. Kxf1 Ne3+ 22. Ke2 Nxg4. (The fork 23. Kf3 is met with 23... Nf6, and 23. h3 is met with 23... Bf6, trading another pair of pieces, creating isolated doubled g-pawns, and weakening White's kingside dark squares. Also, Black is threatening 23... Bxc3!! 24. bxc3 Nxc3+, trading a piece for three pawns, and blowing White's position open even further. It will take White's king to stop the connected passers and the knight to stop its counter part. Once your kingside majority starts moving, the game is over.)

20. Rf1 Ne3! (This wins a pawn by force after 21. Rxd1 Nxd1 where White is forced to play 22. b3 and give up the c-pawn or play anything else and give up the b-pawn. After 20... Rxf1+ 21. Kxf1 Ne3+ 22. Ke2 Nxg4 the material count is the same, but this way White's queenside falls apart faster.)

21. Rxd1 Nxd1 22. Kf1 Nxb2 23. Ke2? Bxc3? (23. Ke2? lost a third pawn to the fork 23... Nxc3+. 24. Kd2 kicking the knight is met with 24... Nd1.)

24. Kf3 Nd2+ 25. Kf4 f6 (Black is threatening g5+, so 26. Nf3 is forced. The best way to continue is 26... Nxf3 27. gxf3 Bb4 and the King will have to come over to the queenside, when you can push your kingside pawns.)