How do I repair the tilt on my artisan table saw ?

I'm not familiar with your saw, but I'm familiar with table saws in general.
The tilting is achieved by a worm screw on the end of the crank handle engaging a partial worm gear on the tilt mechanism.
If all you get is clicking, the worm is jumping out of the teeth on the worm gear. It's likely that the shaft you're turning has slid a bit in its bearing and the far end of the worm is no longer constrained and no longer holds the worm tightly against the worm gear.
I'd say just take the whole thing apart and re-assemble it. In the process, you'll find out how the worm has slipped out of place and you'll see how to put it back where it belongs so that the worm is supported on both ends.