Apart from the intrinsic interest in formulating a consistent, relativistic quantum string theory, its importance stems from the fact (belief) that it may provide a finite quantum theory of all of the interactions in nature, including gravitation. This chapter presents the rules for calculating on-shell tree scattering amplitudes for the open (and closed) bosonic string, using the vertex operators and a propagator whose form is motivated by our experience of calculating scattering amplitudes in (bosonic) quantum field theory. It aims to verify that the (open-string) amplitudes possess the anticipated symmetry under a cyclic permutation of the external particles, and have poles corresponding to the known tachyon, vector states and the whole tower of massive string states. The generalization of these topics to the superstring is addressed. The chapter indicates how scattering amplitudes are calculated in (potentially) realistic theories such as the orbifold and fermionic models.