An emerging solution for prolonging the lifetime of energy constrained relay nodes in wireless networks is to avail the ambient radio-frequency (RF) signal and to simultaneously harvest energy and process information. In this paper, an amplify-and-forward (AF) relaying network is considered, where an energy constrained relay node harvests energy from the received RF signal and uses that harvested energy to forward the source information to the destination. Based on the time switching and power splitting receiver architectures, two relaying protocols, namely, i) time switching-based relaying (TSR) protocol and ii) power splitting-based relaying (PSR) protocol are proposed to enable energy harvesting and information processing at the relay. In order to determine the throughput, analytical expressions for the outage probability and the ergodic capacity are derived for delay-limited and delay-tolerant transmission modes, respectively. The numerical analysis provides practical insights into the effect of various system parameters, such as energy harvesting time, power splitting ratio, source transmission rate, source to relay distance, noise power, and energy harvesting efficiency, on the performance of wireless energy harvesting and information processing using AF relay nodes. In particular, the TSR protocol outperforms the PSR protocol in terms of throughput at relatively low signal-to-noise-ratios and high transmission rate.