It's quite easy to dice using a chef's knife; it's a simple four step process. Step one, square up the vegetable by cutting off the sides. If you're dicing a potato you might peel it first, but with most vegetables peeling is a waste of time because you'll be trimming the peel off with your first cut. Save the trimmings for the stockpot or compost pile.
Step two, make slices of equal widths. If you're doing a ½" dice or french fries, make the slice ½" wide. A standard dice is ¼", while a brunoise would be an eighth or even a sixteenth of an inch.
Step three, make matchsticks, also called julienne. If you are doing this to a potato, you'd be ready for french fries. Just stack the slices so you can cut slices through them at the same width.
To complete the dice, turn the julienne 90° and make equal width cuts across the length.
That's all there is to it.