fireworks tend to use a lot of sky especially at events so a wide angle lens is preferable ( 24mm or similar ) and a tripod is essential
typical settings i would use would be
8 - 9 second exposure
F8 - F11 ( F9 seems fine )
100 iso
to set focus up i would focus on the first firework manually just swinging the focus to infinity is no good because most lenses will allow you to move the focus beyond infinity ( try it for yourself and focus on the moon to see what i mean ) once iv'e gained focus i would just release the shutter when the fireworks start and keep doing so until they stop
i find if you are going to a firework display the fireworks are usually set off thick n fast so 8 or 9 second exposure is plenty
the black card method is great if not a lot of fireworks are set off at the same time allowing you to build a display up but not much use if a whole bunch are repeatedly fired off which is usual at big events
an example of fireworks using a 9 second shutter speed at f9 100 ISO at 24mm on a cropped sensor
i was around 200 - 300 yards away and would have been better off either using a wider angle lens or being another 100 yards further away so don't get too close or you will not be able to get the full display in frame
good luck...