It's easiest to get your hair dyed professionally, but it's more cost effective to do it yourself. The first step is to select the color of brown you want to go with. You also want to make sure the dye you use is a conditioning dye that includes highlights.
Try a semi permanent color first. They are more forgiving, and if you want to return to blond, the color just fades gradually. Pick a warmer, more golden shade, since an ash tone on light hair will come out greenish are steely looking. Try going just 2 shades darker at a time, until you find what you love.
You have two choices, if you want to go with the type of dye available at drugstores: permanent or semi-permanent hair colouring. Semi-permanent fades away after a certain number of washes. Permanent is... obviously... permanent. I'd go first with semi-permanent - see whether you like the look.