BP and Shell are the two biggest oil companies on the London stock market. As two businesses in the same industry, their share prices might typically follow a similar path over time. Every so often, though, BP’s price might go up by much more than Shell’s, or vice versa. When this happens, you could speculate that the two shares will move back into line with each other. This is called a "pairs trade".
To do a pairs trade, you simply buy the low-priced half of the pair and short-sell the high-price half. So, if BP's price has become high compared to Shell's, you simultaneously do a "sell" trade on BP and a "buy" trade on Shell. If the ratio between the two prices then decreases, you make a profit. This can happen either by Shell rising by more than BP, or by Shell falling by less than BP.
The best way to look for potential pairs-trading opportunities is by using charts. You can easily display the ratio of one price to another with a charting software-package. Or you can download the prices for free from Yahoo finance and then use a spreadsheet to plot a graph. The accompanying chart shows BP's share price divided by Shell's over the last decade. When the blue line is at the top of its range, you know that BP is high relative to Shell by past standards.

When researching pair trades, it is vital to look for two assets that genuinely are a pair. As well as finding prices that have had a consistent relationship over time, you should also consider the reasons behind it. Also, just because a price relationship has got out of kilter, that doesn't mean it cannot get even more so. For this reason, choose your stop-loss levels carefully when doing a pairs trade.