Don't put in the dishwasher
Don't use chemicals
If they are really "crap"go online with "gas burner and flame cap". A set of four will cost you about £20. I know someone who keeps a spare set to put on when mother-in law visits!! If you can't find the correct size go online to espares, but a genuine part could cost £20 per ring.
To clean:
Soak in soapy water - Remove debris - buy liberon grade 0000 ultra fine grade steel wool 100G £3.49 from screwfix - rub the cap and polish the burner.
This steel wool can be used to polish glass and antique furniture so it isn't going to make a mess of your burners and rings.
Aluminium will never become as shiny as new unless you spend hours with Brasso afterwards.
Try and remember to soak your burners and rings as soon as you finish cooking, Yea right!!