Cut the chicken crosswise into 1-inch slices, or whatever size cubes you are aiming for.
Cut each slice into cubes, trying to make all sides approximately the same size.
Notes
To make cubing raw chicken easier, before you cut the chicken, freeze it slightly. Placing chicken breasts in the freezer for about 20 minutes allows the meat to firm up a bit. This makes it easier to cut the chicken cleanly and neatly.
If a recipe calls for diced chicken, cut the cubes to about 1/2 inch.
Cubed or diced chicken (cooked or raw) can be stored in a sealed container in the fridge for up to 4 days.
You can freeze cubed chicken (cooked or uncooked) for up to 6 months. Make sure to put it into a freezer proof container or zipper top bag with as little excess space as possible. Label the container and freeze.