I'm going to refer to the stove as the hearth, as I don't have a traditional hearth in my apartment (drat!). When I clean it, I clean off the grime and food stains and I also take time to smudge the area and light a candle on the back of the stove. Sometimes I'll put a candle inside the (clean, electric) oven as well, as a welcoming to the hearth deities, especially Hestia.
I don't have any specific cleaning chants that I use, but I'd love to learn some if anyone knows of any. That's it. I clean and bless the area, but not that often, really. Just whenever I feel it needs a good cleansing.
* Use natural cleaners - I use a mixture of white vinegar, water, and hydrogen peroxide (this mixture can be found on various websites)
* I like to scrub widdershins, and then do a polishing deosil wipe