The previous answer to this question was "use a high pressure
power washer".
I must say that depending on the type of brick, state of the
mortar and condition of the brick itself, using a pressure water
could cause nothing but problems. Some bricks and all mortar are
porous. Using high pressure water will do nothing but force water
deep into the mortar joints and the bricks themselves.
Getting the paint off without damaging the bricks is not an easy
task. Using a stiff bristle (not metal bristles) and warm water
with dishwashing soap is the first thing to try. After that you can
try one of the gel pain strippers or a heat gun and gentle
scraping.
The most important thing is protecting the integrity of the
brick. You can always redo the mortar in certain areas if you
damage it, but you don't want to have to replace bricks.
Sandblasting will remove the outer "coating" of many bricks
exposing the porous internal brick...not good.
If you do have to deal with mortar and tuckpointing and your
brick/mortar is more than 90 years old you cannot use modern
"portland cement" mortar. It's too hard and will ruin the older,
softer bricks. There is a lot of info on mortar and old brick.
Never ever use a portland cement product on older brick and never
use a high pressure washer or sandblast a brick wall of any
age.