When I've done / issued these kinds of tests before in interview, it's usually on a shared notepad - ie you'll be given a link to follow and you can write pseudocode / in the language of your choice - The interview panel will typically be able to see as you type. A lot of the time what I'm trying to ascertain is:
- Does the candidate know basic programming concepts?
- Can they explain the code their writing?
- Is their problem solving process methodical?
Remember, I don't care if your code compiles, or actually runs (unless the interviewer actually stipulates that), I'm looking for your methodology, your thought process. Generally if the candidate says nothing out loud, I'd ask them to talk me through their solution at the end, and ask if they could solve it in any other way (optimisation, trade offs, scaling). Another alternative is that you comment your code as you write, for your own reference and the interview panel's.
You'd be surprised how very simple problems can yield a really solid impression of a candidate's problem solving skills, and raw programming ability. Something like, output a Fibonacci sequence for x iterations is a nice and simple problem, but I've set more complex ones... see here for a list of some to maybe practise yourself.
Don't be afraid to email the person conducting the interview and ask for clarification on how the programming test will be issued, ie, do you need an account on anything? - it shows a bit of thinking ahead, if nothing else!
Edit: Pierre's comment is another possibility, I actually had no idea that skype had interview specific functionality!