Hummingbirds only come through my neck of the woods for a few weeks per year so when I was visiting family on the west coast I took the opportunity to try some shots of a family member's feeder that has hummingbirds virtually year round. They're certainly not as nice as many hummingbirds photos posted here but as a first attempt I was happy with the outcome.
These were all taken off a tripod with a remote shutter release, 5D Mark III, 100-400 lens,1/4000 @ ISO 3200.
Nice. Now to get closer. With a tripod and that lens, you should be able to get right in there and prefocus on an area the birds will go to (just a bit away from the feeder openings).