First thing you need to do is establish what is causing your haze. Common types off the top of my head:
yeast haze (allow the yeast to drop or use a finning agent – gelatin / biofine in the bottles with your priming sugar or into your keg – not sure of its affect on natural carbonation)
protein haze (use kettle fininings – whirlfloc / irish moss)
hop haze (you would probably know if this was your haze issue)
bacteria infection haze ( Let’s just hop it’s not this one)
unconverted starches due to a poorly executed mash (if you’re doing extract, don’t worry about this one)
Whether or not quickly chilling the wort allows for a clearer beer is up in the air. Same with transferring all the gunk from the kettle to fermenter. Personally I feel both are “old brewer’s tales”. Doesn’t mean you shouldn’t do them, though. Keeping out the trub helps beer flavor and chilling fast reduces your risk of infection.
Part of my brew day is being sure the beer is clear at every possible step – once the mash is converted it’s quite clear and then at the end of the boil it’s crystal clear. Personally I transfer nothing but the crystal clear wort into my fermenter. I do this by draining from about three inches off the bottom of the kettle – all the trub is below that level.
If you’re doing extract batches, use 1 tab of whirfloc in the last 1 min of the boil every time, that’s about all you can do. I highly recommend whrifloc as a possible easy solution to your haze problem.
Rumor has it that it can be a bit difficult to get a crystal clear beer with extract. But you should be able to at least see your finger through the glass.