Welcome to the forum, I hope you enjoy KOF. Fortunately, KOF13 is a great game to start the series with.
Regarding your question, my personal answer is "combos".
You would want to spend a lot of time experimenting with your characters. The process is very fun and enjoyable. Generally, the first 5 trials of each character in Mission mode gives you a general idea of what is possible to do with the character, but they don't represent the optimum combos. You would still need to find the right combos that suit your style. Ignore the more advanced trials for now. They are just meant to drive you nuts.
Even after learning combos in Practice mode, you would still need to get used to them in actual matches. Arcade / Story mode will help a lot on that regard.
I don't need to mention this, but Tutorial mode should be your very first step before all of that. You can also check the videos posted
here. They are very informative, and they even cover some basics for the combos system.
You would also need to get used to the game's "flow". A lot of Capcom players struggle with KOF, so try to give it a chance and expect it to take some time with you. You may want to focus on the different jump types and rolling.
I would like to add one thing. There are few things to consider when picking up your team.
This thread contains some valuable tips regarding that.
Finally, you can use these two guides for some general information, as well as character-specific details and tips:
http://dreamcancel.com/wiki/index.php?title=The_King_of_Fighters_XIIIhttp://wiki.shoryuken.com/The_King_of_Fighters_XIIII hope that helps.
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(and EX) grab has full armor during initial animation
grabs opponent while on floor (guaranteed after qcf x2 K DM and normal grabs if opponent doesn't do a safe fall)
(1 hit) > 
