Easy. Go to your local eclectronics store or supermarket(Wal-Mart, Hobby Shop, Canadian Tie, Home Depot, Home Hardware, etc) and buy a can of compressed air for cleaning electronics. They cost $7-$20 and are ment to blow dust out of buttons. The DSi, for reason, is particularly succeptable to getting crap in the Shoulder Buttons, and a Can of Air can be priceless for this.
Without spending any money, you could just blow into it mash the button until it works.
The other option(though not recommended) is to take an Air Compressor to it. But if you do, barely pull the trigger, you could break something inside the device using this method.
Hope this helped. Being a previous DSi owner, I had to go through the same thing, and so did a lot of others. My 3DS does this too, though not quite as often.
Blow it for 10 seconds. The L and R buttons on my dsi broke also. But anyways I fixed it and this time it fell and my dsi broke. So all I have right now is 3ds, Iphone, Ipad, Wii and Dsi LL
Believe in yourself. And if not, you might never achieve the things you want to do
Cool. I really do recommend getting a can of air though. I had dirt in my 3DS speakers once, and couldn't get it out by blowing on it. Can of Air: *psshht* Done. That quick.
I had that same problem, and this is how I fixed it: blow into whichever button is screwy. Make sure you don't spit in it though. DSi's apparently had a hardware defect on the buttons in which they were not sealed enough to the bezel to prevent dust from accumulating. If you do this a few times a year, it should be good.