We give a realization of the Kirillov-Reshetikhin crystal B^1,s for sl^{^}_n using Nakajima monomials using the crystal structure given by Kashiwara. We describe the tensor product \bigotimes_i=1^N B^1,s_i in terms of a shift of indices, allowing us to recover the Kyoto path model. We give a description of the limit of the coherent family of crystals {B^1,s}_s=1^\infty using Nakajima monomials, which allows us to recover the path model for B(\infty). Additionally, we realize the KR crystals B^r,1 for sl^{^}_n using Nakajima monomials.