In a multi-stage device, the "trigger" is simply the first stage ---a fission device.
As Abaddon correctly states, a sufficiently violent fission reaction can be acheived both with highly enriched uranium and weapons grade plutonium.
(Of the two, the latter is more preferable because it can be produced in any quantity desired in a breeder reactor, but this only applies to nations that are already recognized nuclear powers. Nations that cannot openly operate a reactor of any type (e.g. Iran, Libya) must try to take the uranium route.)
Typically, the energy released by the trigger slams into a mantle of heavy water producing a secondary fusion reaction. The fusion reaction releases an extremely dense flux of neutrons that can in turn be harnessed to produce a tertiary fission reaction even in unenriched uranium.