Depends on whether or not you are looking for understanding, or just for a formula to use for a particular case.
For the latter: the e.m.f. ('voltage'), ε, generated in a straight wire of length L moving at speed v at right angles to its own length and to a magnetic field of flux density B is ε = BLv.
If the wire is part of a circuit of resistance R, the current, I, will be I = BLv / R. But the rest of the circuit must stay stationary while the wire of length L moves. For example, the wire may slide along stationary rails, making contact with them at each end of the wire. The rails connect to the rest of the circuit. If the whole of the circuit, including the wire, moves all together, there will be no emf and no current.
To understand why there is no emf in a circuit which moves without turning through a uniform field requires a proper understanding of electromagnetic induction. You need, in particular, to understand what is meant by flux linkage and cutting of flux.