How does Meimei trick her mother into letting her play in her first tournament?

Meimei, otherwise known as Waverly, tricks her mother into letting her play in a chess tournament by appealing to her mother's sense of family honor as well as to her sense of competition.

Let's take a look at that part in the story:

A man who watched me play in the park suggested that my mother allow me to play in local chess tournaments. My mother smiled graciously, an answer that meant nothing. I desperately wanted to go, but I bit back my tongue. I knew she would not let me play among strangers. So as we walked home I said in a small voice that I didn’t want to play in the local tournament. They would have American rules. If I lost, I would bring shame on my family.

 “Is shame you fall down nobody push you,” said my mother.

During my first tournament, my mother sat with me in the front row as I waited for my turn.

As you can see, Waverly really wants to play in a tournament, but she knows that her mom probably won't be okay with Waverly playing with strangers. She could just ask, "Ma, can I play in a tournament? I really want to." But she understands that this approach wouldn't work with her strict mother.

Though she's not quite eight years old, Waverly pulls off some serious manipulation of her mom on the way home: she uses reverse psychology, acting like she doesn't want to play because any losses might shame the family. Waverly's mom doesn't like to see her daughter so easily defeated--shame and success are serious, prominent issues in Waverly's mom's mind-- and the next thing readers find out is that both Waverly and her mom are at the tournament!

You might wonder why Waverly brought up the idea of "American rules" when she mentioned the tournament to her mother. Remember that earlier in the story, Waverly's mom had read through the booklet of chess rules and announced to her children that the rules for the game were much like the rules for living successfully in American society. Waverly's mom, then, prides herself on determining what the "rules" are and in using them to achieve social success for her own family. Waverly remembers this, and in the passage above, when she's walking home with her mom, Waverly is basically saying, "We can't follow American rules or succeed at life in America, so I shouldn't play in the tournament," and Waverly's mom is basically responding with "Oh yes we can! Let's sign you up for the tournament!"

So, Waverly was able to appeal to her mom's sense of pride, and to her eagerness to "win" at the game of life in American society.