The first thing you need to do is clean all the gunk and old layers of dressing off your tyres. A stiff brush and lots of grease cutting soapy wash (you can buy proprietary tyres cleaners but they are not really necessary). Scrub your tyres really well. Dry them.
Now you have a good platform to start from.
Apply a product like Meguiars Endurance Tyre Protectant (It's a GEL) with a dedicated sponge applicator. Be warned, it's mucky so wear latex goves if you have any.
Wipe it well in (don't let it run and drip all over the place). If you want extremely shiny tyres apply a second or even a third coat.
Mate, you will have shiny tyres.
An alternative is Meguiars NXT Insane Shine Tyre Spray which you can get in an aerosol or a spray bottle.
But, whatever you use, you must get the tyres cleaned up first.
Oh, and when you're finished you better polish up those alloys to complement the tyres