A magnetic field will curve the trajectory of charged particles (for more details click here). Negatively charged particles are curved in one direction (click on picture and move cursor over active area A), positive particles in the opposite direction (move cursor over active area B).
Usually it is not necessary to be told which way is field pointing - the picture already contains the answer. The little curly tracks are produced by electrons which are knocked out of the atoms by charged particles passing by - so the magnetic field points into the screen.
Electrons spiral because they are much lighter than all other charged particles
and lose energy quickly by another process called bremsstrahlung (for more
details click here).
(Anti-electrons or positrons will also spiral. More on this later.)