The L and R buttons, also called the "shoulder buttons," are located on the back of the system on each corner; L on the left side, and R on the right. The location of these buttons are the same across all versions of the DS.
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(upper buttons) L R L R L L R R A on the cup selection screen
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Weirdly enough, close your DS and cover the broken button with your mouth and blow.. It will get it working. I dont know why this works (dust?) but it gets them working for a while.
Many DS games will reset their save data if you hold down the A, B, X, Y, L and R buttons (simultaneously) when the game is starting up.
Well, you can turn it off and then back on ...but if you don't want to do that, most Nintendo games have a soft reset ~L + R + start + select