For a category A machine (up to 125cc and 11kW power output) you must first satisfactorily complete a CBT course. The CBT will last two years, you must display L plates, can't go on motorways and can't carry passengers.
For a category P machine (up to 50cc legally defined as a moped) since you passed your car test before Feb 2001, the DVLA will also have given you a full P entitlement. This means it's just like having passed a test on a moped, you can dispense with L plates, CBTs and may carry passengers (but still not use motorways where there is a 50cc lower limit).
Those drivers who passed their car test after Feb 2001 will receive a full P category which only becomes valid after obtaining a CBT certificate. This will then last for their driving career. They can also do this the other way round i.e. pass a driving test whilst holding a current CBT certificate.