Most psychostimulants serve as exogenous ligands for the catecholamine transporters - in laymans terms, the presynaptic pumps which vaccum any leftover dopamine or norepinephrine within the synaptic cleft back into storage. The prototypic stimulant in this case binds to the catecholamine transporter, serving two functions:
1) inhibit its reuptake of neurotransmitters.
2) causes the transporter to function in reverse by pumping catecholamines outward into the synaptic cleft.
The overall increased concentrations of synaptic catecholamines leads to a major increase in catecholamine signaling, inducing arousal of the sympathetic nervous system and increased mesolimbic "reward" activity.
Many psychostimulants (including amphetamine and cocaine) also act as ligands at the serotonin transporter; serving the same function of inhibiting reuptake, and/or reversing transporter flow. In fact, there is an entire family of atypical psychostimulant compounds (which includes most notably MDMA/ecstasy), that exhibit a unique set of empathogenic and psychedelic properties. This has been linked to their relatively potent serotonergic properties.