How does the Bohm interpretation/pilot wave theory explain particles getting spontaneously created and destroyed? Pilot wave theory says that classical particles are riding on waves.
Quantum field theory says that particles are the excitations of a field.
Both of these descriptions seem like essentially the same thing, if we equate pilot waves with quantum fields. What are the differences?
Also, the quantum field description allows particles to dissolve back into the field, and also to be spontaneously created out of the field. This has been observed in experiments. How does the pilot wave description explain this?
 A: 
if we equate pilot waves with quantum fields. What are the differences?

The fields of quantum field theory are not associated with a specific particle, they are generic over space and time, like a coordinate system , on which creation and annihilation operators operate to create a given particle. The pilot waves are connected with the given particle. In addition the theory is not Lorenz invariant, whereas field theory is by construction.

Also, the quantum field description allows particles to dissolve back into the field,

this is a misunderstanding, the fields are invariant, nothing can dissolve into them,

and also to be spontaneously created out of the field.

Energy must be supplied to be able to create a pair of particle anti-partcle

This has been observed in experiments.

Only with incoming energy . See this entry.

How does the pilot wave description explain this?

Pair production needs par excelence special relativity , and pilot theory is not good at special relativity. There is still research on this though. If they succeed, the connection with QFT  though will not be as simple as you envisage.
