How can I attach a garden hose to my sink faucet?
Yes, but it won't be pretty. There's a fitting designed to let you hook up a dishwasher to a sink faucet. They come in both temporary and permanent varieties. Don't ignore the removable kind as that might be exactly what you need if your hose use is just occasional. From there, you can get another fitting to step up the dishwasher connection to a garden hose size connection.

Just realize that you're not going to get much volume/pressure out of a sink.

If you don't need a garden hose per-se but just a hose-like think for short range use, investigate a bath store like Bed Bath and Beyond. There exist rubber hand-held shower products that are designed to fit on to the end of a bath spout or screw on to a sink.