I'm assuming you mean the original DS and that is what I've based this answer on (have never done DS Lite so wouldn't know) the solution is dead easy first buy a replacement screen off e bay for approx £10
Once you've got your screen use a needle to remove the four rubber covers on the front of the ds (round the top screen 2 are raised the other 2 flat) this will reveal 4 little screws. remove them with a small jewellers style screwdriver. Once these are removed you should then be able to prise the back cover off. Once the back cover is off, with the DS closed and the hinges towards you looking down on an open back you should see 2 cicuit boards left and right, remove the right one. slowly turn it over underneath you should see a ribbon connector you need to carefully slide out the two little black 'tags' either side of the ribbon (please note they do NOT need to be removed fully just enough to release pressure on theribbon connector enabling you to remove it). Once you've done this you can then slowly prise the broken screen from it's recess. Fitting the new one is the exact reverse of removing! Only real tricky bit is the little clips either side of the ribbon be VERY carefull not to be too forceful with them or they may break. Also ensure that the ribbon connector of your new screen is pushed in fully before re inserting the clips. Always a good idea to check that it works before putting the back back on ;)you want any more help feel free to e-mail me jonashuk@aol.com
Jon Nash, March 2008