From a practical standpoint, with most brokers, you simply attempt to sell the stock, and the order is either accepted or rejected. Many brokers will automatically determine that it is a short-sale, since you don't own the shares. Others, you may have to specifically designate the order to "Sell Short" instead of "Sell".
For the overwhelming majority of stocks and brokers, you will be able to short at least 50K shares. This changes, of course, for stocks that are "in play" and are being heavily shorted. A lot of those become "hard to borrow". Some brokers will simply not allow them to be shorted. Others, you may be able to call their "stock loan" department and pay a per-share rate per day to borrow them.
In unusual circumstances, there is some risk of a forced "buy-in". This means you can be short a stock that you are no longer allowed to be short, and the broker will force you to buy back the stock. This usually happens with a day or two's notice, though I've heard of it happening intra-day, too. It usually is accompanied by a rally in the stock's price as everyone is forced to cover their shorts
