Board size and first move apply from the next game.
Take turns drawing one line between two dots that are next to each other, across or down. Close the fourth side of a box and it's yours: your mark goes in it and you draw again. When every line is drawn, whoever owns more boxes wins.
Drawing the third side of a box lets your opponent close it. Early on, avoid drawing third sides.
Late in the game every line gives something away, and boxes come in chains: rows of boxes that can all be taken one after another. Try to give away the short chains, and make your opponent be the one who has to open the long ones.
When you're taking a long chain, you can stop two boxes short: draw the line at the far end instead, leaving those two for your opponent. They take the two boxes, but then they must open the next chain for you.
Tap anywhere near a line to draw it. On small screens the first tap marks the line and a second tap draws it (change this in the ⋯ menu, where you'll also find Undo). Your boxes get a blue cross; your opponent's get a red circle.