One cell, Why would you?
Do you mean you have several isolated cells, or simply one cell in a dish/on a coverslip.
My first piece of advice might be: can you produce more cells, as most cells don't survive very well entirely on their own
Failing that, you have some techniques available to you still. You could image it (load with fluorescent indicator dye), and you could immunostain it. I don't think PCR or anything that involves extractions would be possible with a cell (so no western blotting, RNA analysis etc).
If you need more info on live cell imaging or immunostaining then just ask
All the best, Cakeman