How am I going to play Cchess?

I wonder if I can (even) win because it's the first time I'm going to play a chess game in a tournament.

I would suggest adding "even" here because it adds to the feeling of "first time"

I typically just see "play chess"

I didn't change it in the first sentence because that sentence was focused on the game aspect (competing against Alexa) and this sentence was focused on the act of playing

I'm going to look for advices in some books about chess and I'm going to analyze my games and movements to develop a better game ion the chessboard.

Advice is uncountable

I think a more appropriate word would be "a better strategy on the chessboard" but as it is not wrong I did not change it