How do I use NPV analysis of an investment to show that it is just a "break even" proposition?

I'm not quite sure what they're having you do there. A net present value is the difference between the present value of the future cash flows and the value of the current investment. If they are equal, or very close to equal, then you could consider that you're breaking even on it.

But there isn't any difference in how it would be done from a normal NPV that isn't breaking even.

Break-even analysis shows a no-profit or no-loss situation. It has nothing to do with NPV. NPV - Net Present Value, shows the value creation for an organization if a particular investment is undertaken. In NPV analysis we discount all the cash flows using some discounting factor (Eg - Projects required rate of return) and come up with a figure which represents, if positive, the new value addition. In other words let us suppose NPV of a particulat project USD 1,000. This means you add cash worth of USD 1,000 to the organization today.
On the other hand Break-even analysis is more of management tool to decide on, lets say, the number of units to be sold to become in no-profit or no-loss situation.
Thus NPV technique should not be used in conventional break-even analysis.

Break-even analysis shows a no-profit or no-loss situation. It has nothing to do with NPV.

Agreed... and when I hear "break even" I immediately think of the traditional "BE analysis", to which you refer. But I doubt the wording of OP's question was accidental--it sounds like they have in mind a BE concept that's NPV-related. If so, I'm with Morgaine on this one.

If someone tells me that a project is "just breaking even, in a NPV sense", my first thought is that the project is exactly earning the required hurdle rate--no more, no less.

In an EVA (Stern Stewart's Economic Value Added) sense, a project with a zero NPV would be considered "breaking even".