For drilling soft metals like silver and copper, you can use hardened steel drill bits that are sold at hardware stores, if you can find a small enough size.

Diamond coated bits are good if you are drilling something harder, such as glass or a harder metal. I get diamond bits from jewelry supply companies like Frei and Borel (which is local for me) or Rio Grande by mail order. You can also use diamond bits to drill soft metals, but they tend to cost more than hardened steel bits.

Drill bits last longer and work better if they are lubricated. My favorite way to lubricate while drilling is to have a small dish of water nearby and start with a drop of water on the spot I’m going to drill. I dip the bit in the water, and whenever it starts to dry up, I dip it again. This also helps prevent dust from getting into the air, so it makes the process safer, and it keeps the bit and the metal from overheating.

I use a pointy object to make a little dimple in the metal right where I want to drill, which makes it a lot easier to get started.