We develop and analytically study the performances of three relay selection techniques for a two-hop decode-and-forward (DF) cooperative communication system in a large wireless sensor network with uniformly distributed nodes. It is assumed that there is no central processing unit to optimally select the relay and that the nodes use their locally available knowledge, that is, their distances from the source as well as their backward channel gains, to compete with one another to acquire the relaying status. The relay selection schemes are compared in terms of their fairness and energy efficiency. Taking into account both the fading effect and the nodes' locations distribution, the end-to-end outage probabilities of all relay selection schemes are derived and discussed. In particular, it is proved that when the source transmission power is high enough, the outage performance is independent from the scheme used to select the relay. Moreover, when the node intensity is large enough, the outage probability of the optimal relay selection scheme is almost the same as that of its suboptimal but more energy-efficient counterpart that uses the nearest node to the source as the relay. Computer simulations are used to validate the analytical results.