The strategy is to buy the convertible bond, and short the equity into which it can be converted. This will be profitable if the embedded option is under-priced relative to the underlying. It is possible to reverse this strategy (go long on the underlying and short on the bond), but this is less common. The latter is also often fairly expensive, even when the opportunity does arise to use it, because it is likely to have negative carry.
As ratio of short sales of the equity is usually chosen to delta hedge the value of the embedded option. This provides a dynamic hedge. The major problems with this are the cost of short selling, and the risk that arises because dynamic hedges are rarely perfect.
Convertible arbitrage positions are also exposed to other risks, such as the default risk of the convertible. For these reasons, despite the hedging, convertible arbitrage can make losses. There have been periods when convertible arbitrage funds have made sustained losses, as can be seen by looking at a convertible arbitrage index.