Neuronal oscillatory activity has been reported in relation to a wide range of cognitive processes including the encoding of external stimuli, attention, and learning. Although the specific role of these oscillations has yet to be determined, it is clear that neuronal oscillations are abundant in the central nervous system. This raises the question of the origin of these oscillations: are the mechanisms for generating these oscillations genetically hard-wired or can they be acquired via a learning process? Here, we study the conditions under which oscillatory activity emerges through a process of spike timing dependent plasticity (STDP) in a feed-forward architecture. First, we analyze the effect of oscillations on STDP-driven synaptic dynamics of a single synapse, and study how the parameters that characterize the STDP rule and the oscillations affect the resultant synaptic weight. Next, we analyze STDP-driven synaptic dynamics of a pre-synaptic population of neurons onto a single post-synaptic cell. The pre-synaptic neural population is assumed to be oscillating at the same frequency, albeit with different phases, such that the net activity of the pre-synaptic population is constant in time. Thus, in the homogeneous case in which all synapses are equal, the post-synaptic neuron receives constant input and hence does not oscillate. To investigate the transition to oscillatory activity, we develop a mean-field Fokker-Planck approximation of the synaptic dynamics. We analyze the conditions causing the homogeneous solution to lose its stability. The findings show that oscillatory activity appears through a mechanism of spontaneous symmetry breaking. However, in the general case the homogeneous solution is unstable, and the synaptic dynamics does not converge to a different fixed point, but rather to a limit cycle. We show how the temporal structure of the STDP rule determines the stability of the homogeneous solution and the drift velocity of the limit cycle. 