Picross is actually a pretty simple game. But it's called a puzzle game for a reason, and it can get pretty hard.
So here's how to play:
There's the game grid, and numbers surrounding it.
If the first number on top says 3, that means that somewhere along that column of the grid are 3 blocks in a row that need to be filled, and all of the blocks before or after are left blank.
Now let's say the second number on top is a 2 1, that means that somewhere along that column are 2 blocks in a row that need filling, and then 1 block that is after it, but not right after it (otherwise the number would just be 3). So the next one is at least two spaces after it.
You just follow this for each side until you figure it out and win.
When you want to fill in a block of the grid, make sure that the pencil icon of the top-left corner of the touch-screen is selected.
Select the X icon below it if you want to place Xes on a block of the grid to remind you not to fill that block in.
And of course in the game you catch Pokemon, and you set them in your party. You can use a Pokemon's special ability to help you in the game (by clicking the Poke Ball in the top right corner of the touch-screen while in a game, and then selecting whichever Pokemon you want to use).
Hope I helped! Comment if you're still confused on anything.