There are many resources out there on shorting, but I'll give a brief overview.
Shorting is just the opposite of buying. If you think a stock will go down, you borrow it from your broker (more on that later) and sell it now. You buy it back later, when the price has hopefully gone down.
The uptick restriction means that you cannot short a stock until a trade with a higher or the same price compared to the previous trade. That is, if the price is plummeting down without a stop, you can't short it. If you place a market order, it may be filled at the first pause. In practice, this is only important with extremely volatile stocks that are breaking down rapidly - in those situations, if you enter a market order to short, you may end up with a much, much worse price than you expected. It's rare, but it is a danger.
Shorting is considered more-short term and risky than buying, because when you buy the worst you can lose is 100%, while if you short, and for some reason the stock triples, you lose 200% (of course, you'll get a margin call long before that). Also, stocks tend to go up more steadily than they go down (stocks are moving up or sideways 2/3 of the time, and down 1/3 of the time, roughly). However, the advantage of shorting is that stocks tend to move down faster than up, because of fear. Also, if it's a bear market, many people prefer to be active making money by shorting rather than sitting on their heads waiting for the bull.
When you short, you are borrowing the security from your broker, who is borrowing it from another customer who is holding it. That means that with some brokers you will not be able to short some stocks, and most newer stocks cannot be shorted at all. The downside of this is that the stock could be called away, so that you have to buy it back immediately, sometimes at a very inconvenient time. In practice, this doesn't seem to be much of a problem.
People who short are naturally more short-term reactive than buyers, because prices are more volatile moving down than up. Generally, they move down in waves, so that you enter at the top and exit at the bottom. You then re-enter at the top of the next wave (although this is of course difficult in practice). A short squeeze is when a trader decides to bid (buy) up the stock enough to scare the shorts into covering at a loss. This can happen frequently with different stocks. The best defense is to only short stocks that have good liquidity (large daily volume). You could also just close you eyes and hold out against the squeeze, but that's suicidal. In any case, when you short you generally reverse the common wisdom of "take your losses quickly and your profits slowly." Shorting means taking both relatively quickly. The most often quoted figure for a short of less than a month is 20-30% maximum profit before you close the trade, because stocks can shoot back up in a mini-rally quite easily and rapidly.
I won't take about dividends or interest (holding) costs, because I'm not an expert on that, and I rarely short long enough to be affected. However, I will point out that your equity increases as the stock prices goes down, which is the reverse of buying stock.
Lastly, I will point out that, in general, unless you're an expert or obsessed with shorting, you should only short in bear markets. While you can still make good money shorting in a bear market, the real price is the opportunity cost - you can make a lot more buying a bull market.