Bitcoinica does (or did) offer short selling, but the question is how?
If I fund my account with 100 BTC and I want to short BTC, can I do that, or do I need USD to do that?
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Short selling is essentially an agreement between you and Bitcoinica where Bitcoinica pays you if the BTC/USD price decreases, and you pay them if the price increases, in an amount equal to the price difference multiplied by the number of bitcoins you sold short.
Presumably you trust Bitcoinica to hold up its end of the deal, but they don't know you and don't trust you, so they require you to make a deposit which they deem more than enough to be able to cover your obligations. It may happen that when the price changes they are no longer confident your deposit is enough; they will then do a forced liquidation, settling the agreement up to this point and only allowing you to make a smaller agreement going forward.
The deposit can be in either BTC or USD. If you have BTC, however, you may want to consider first selling the BTC (which is functionally equivalent to taking a short position), which may be done cheaper than in Bitcoinica, and then short-sell on Bitcoinica.
An alternative view of short-selling is that you borrow bitcoins from Bitcoinica, offering a deposit as collateral, and then selling them. With Bitcoinica out of the picture for now, short-selling can be done by literally finding someone to borrow bitcoins from.
You can also learn more about Margin trading in general on Wikipedia.