I don't technically live in a studio. But you'd never know that by looking at the size of my kitchen. I have literally two feet of usable counter space, one foot on each side of the sink. Yet somehow, my boyfriend and I have made it work.
We've regularly thrown parties for 15+ people (during which our guests marvel at our synchronized preparation), and cook or bake at home on a fairly consistent basis. Like all other forms of small living, the trick is to make the most of what you have and to eliminate all that you don't really need. For me, it's also about keeping the color palette tight (since most everything we have is out and will be seen) and reigning in the impulse to buy appliances that I can do without. (I would love to have Kitchen-Aid stand mixer, but can't afford the space to store it.)
The owners of these studio kitchens from our House Tours understand the effort it takes to live large in a small space. Some have older kitchens with architectural quirks, and some have done their best to add quirk to an otherwise bland space. (One even had to go so far as to carve out a kitchen where there previously wasn't one!) But each has designed their kitchen with style, ingenuity and care.
(Images: as linked above)