The accelerating voltage in a cathode ray tube
It's done with a transformer.  These devices convert AC electrical power at one voltage x current combination to a different voltage x current combination.

Of course the power out can't exceed the power in.  In practice, the power out will be less than the power in due to losses.  For example, let's say your CRT requires 1 mA beam current at 10 kV, which comes out to 10 W.  This could in theory be generated by a transformer that takes 100 V at 100 mA in.  In reality it will take more current than that since the conversion won't be 100% efficient.

Stepping up voltage by such a large ratio has issues, so a special type of transformer method is employed in CRTs called flyback.  The input voltage is applied to the primary of the transformer with the secondary effectively open.  The primary therefore acts like a inductor, and the current builds up linearly.  When the current (and therefore the energy stored in the transformer core) has built up sufficiently, the current it cut off as quickly as possible.  The energy has to go somewhere, and comes out as a pulse on the secondary.

This process is performed at high enough frequency to transfer the required power thru the transformer.  In old televisions, the pulses were synchronized with the horizontal scans, which occurred at about 16 kHz rate.

Car ignitions work on the same principle.  The ignition coil is a flyback transformer.  The points apply 12 to the primary.  When they open, a pulse of high voltage comes out the secondary.  Nowadays there is a transistor doing the switching instead of mechanical contacts, but the principle is the same.