The tried and true way is a huge current pulse from a capacitor bank through some sort of magnetic antenna. Electronic means have the advantage of being multi-use, but have a significant recharge time between shots. Any chemical explosive produces a small EMP during detonation. To enhance the effect you may use a layered spherical explosive, slow weak explosive on the outside ignited first, and a fast, powerful explosive at the core, detonated last. The shock from the core explosive causes a huge compression wave to be sent through the plasma generated by the shell explosive, electrons and ions are put through a violent acceleration, hence you get a EM transient.
Many configurations are possible, imploding devices, exploding devices, linear shock devices, etc.
Typical kill zones of about 10 metres from grenade sized devices, larger devices physically damage an area larger than the EMP kill zone unless imploding is used. The FCG is initialized by a simple capacitor bank discharge. Daisy chaining of FCGs is also possible. Typically these devices are limited to low frequency RF output because of their rise time. They can be used as one shot power supplies for higher frequency oscillators.