You need minerals in the water for a couple reasons.
1. You need them to help establish the correct mash pH.
2. You need certain minerals for yeast health (specifically calcium)
3. You need the balance of certain minerals for flavor (specifically Cl:SO4 ratio)
So, brewing with pure distilled water would put you in a position to brew very light beers, up to about 10 SRM. Anything above that would drive the mash pH too low and you are in danger of extracting off flavors. You would also be 'starving' your yeast of Ca and Mg (Ca and Mg are specifically important in flocculation).
For brewing with practically distilled water, I see two approaches:
1. Use 5.2 in the mash and add enough salts to reach 50-100ppm Ca for yeast health. You would chose CaS04 or CaCl as to select your Cl:S04 ratio. (Using some MgS04 would not be a bad idea either).
2. Use only slats and build the water to "lock" the mash pH in the correct range and establish the correct amount of Ca and Mg for the yeast.
#2 will be cheaper as salts are much cheaper than the 5.2 but #1 might be easier at the beginning as you do not have to change your salt additions for every beer.
Here are some resources that explain how water composition affects beer:
http://www.howtobrew.com/section3/chapter15-1.html
http://thebrewingnetwork.com/shows/497
http://thebrewingnetwork.com/shows/500
http://thebrewingnetwork.com/shows/508
http://thebrewingnetwork.com/shows/513
(Also, I would be surprised if you don't have something in the water already. Most water systems add something to the water even if the source is practically distilled. For example, I would expect they would adjust the pH to >7 and buffer it there with bicarbonate to protect the pipes, etc.)