I often take shots like this when I am visiting my parents, they have lots of bird feeders in the garden. I found any shutter speeds under 1/100s were just too slow and I used the largest aperture my (rubbish) lens would allow to get rid of the messy background. I set the tripod up and just focused on the feeder until the birds came. Make sure you turn off any beeps etc on your camera and if you wrap as much of the camera as you can in a jumper or something similar you can insulate it and try and muffle some of the sound of the shutter which normally scares them off!

Exposure: 0.01 sec (1/100)
Aperture: f/5.6
Focal Length: 270 mm