Where do you get the tool they use at the Genius Bar to remove SIM cards?

Solution 1:

If you purchase an international or unlocked iPhone, it comes with this SIM ejection tool. They cannot be purchased from Apple, however they are sold on eBay/Amazon/etc.

Solution 2:

The "Apple SIM ejector" is a glorified paperclip. A much better (and more comfortable) tool is a 0.8mm hex driver. Find the precision tools section of your local hardware store and get one that fits. Do NOT get a pointy-end driver like Phillips. Hex drivers have flat ends and smooth sides.

And don't use metal objects to clean out the connector - a toothpick won't scratch up the electrical connections.