Everyone who plays with LEGO bricks knows they're studded, square-edged things. Very rarely can they be imagined as something to form a round object with. However, making a ball or sphere out of LEGO bricks is surprisingly simple to do if you offset the bricks correctly. With some careful planning, you can make an extremely impressive looking LEGO ball.
Build a circle out of LEGO bricks on your base plate. Start on the left side of the base plate, and build to the intended diameter of the sphere. Start near the edge, placing wide bricks to make a 5-stud long side. Above and below, offset another 2-stud wide brick to the right by one stud. Repeat that pattern once more to create an arc that represents one-fourth of the ball's circumference. Attach more bricks to duplicate that curve all the way around and fill in the circle.
This ring becomes the middle of the sphere itself. Use mostly larger pieces, so you create a solid hemisphere.
Build a second layer on top of the circle. Make this disc the same diameter, but set the curved edges to be a stud shorter than the lower row.
Repeat Step 2, making a third layer that's around the same size, but contoured to be slightly smaller than the row below it.
Add three more layers, each of which is 1-stud smaller on all sides than the row below it.
Attach the topmost layer, which must be 2-studs smaller on all sides than the disc just below it. Look at the piece from the sides, and it should look like a hemisphere. If it doesn't, make adjustments.
Gently pull the hemisphere off of the plate. All of the LEGO bricks must come off with it. If you're having trouble, try flipping the entire model upside down and carefully bending the plate to remove it.
Repeat steps 1 through 5 in reverse to build another hemisphere, but upside-down. Beginning with what was the top layer, grow outward until your final layer is the same diameter as the first disc in Step 1. Duplicate the contours of the other hemisphere.
Take the second hemisphere off of the plate. Connect the two hemispheres, lining up the widest plates on both of them. Press the top half onto the bottom half.
These directions are intended for a 6-inch diameter sphere. If you start with a 6-inch ball, you'll have the theory down so you can apply it to other designs. For a clearer picture of what the rings should look like, consult the patterns on the Brillig website. Apply that design to whatever diameter you're using.