Buying NO contracts is probably an easier way for a majority of people to initially figure out what is happening. Imagine that when you sell a contract you don't own, that you automatically buy (from the "bank") a pair of YES and NO contracts (the price of the pair always adds up to a fixed amount - in the case of Boolean claims, that value is 1). Your trade then amounts to selling the YES part of that pair and keeping the NO contract.
Selling short a contract is probably an easier way to think of it when you are actually trading, since it avoids the need to mentally convert between NO prices and YES prices. Forget about NO contracts, and simply treat selling a contract you don't own as going into debt that many YES contracts (or owning a negative number of contracts).
Your cash balance looks a bit different under this representation; some of your cash is classified as "restricted cash" to create a result that is equivalent to having bought a pair of YES an NO contracts.
Prices are expressed in terms of YES contracts almost everywhere. The list of holdings page offers an option to switch between a buying (going long)/selling short YES contracts representation (the default) and a YES/NO contract representation.