Most people use their mobile phones to take photos these days and many now come with very good cameras and zooms.
Set your bird feeder up close to a window and rest your phone on something to get a steady shot. If you have a DSLR use a telephoto lens on a decent focal length, like a 300mm-500mm. When using a long lens make sure it's on a tripod or if shooting through an open window rest it on a beanbag. For feeder or mid-air antics you’ll need a fast shutter speed to capture the birds in flight, around 1/2000. Check your camera settings such as ISO and aperture will allow for this.