First of all, an alpha particle consists of two protons and two neutrons (similar to a Helium atom). When an atom emits an alpha particle, its nucleus loses two protons and two neutrons. And its total mass decreases by 4 atomic mass units.(As mass of a proton or a neutron is 1 amu)
There are two kinds of beta emissions (or particles) positron or electron.
When an atom emits a [tex]{ \beta }^{ + }[/tex] (positron) particle, actually one if its protons releases the particle. Since a positron's charge is positive, when the atom releases a positron it loses its positive charge and turns into a neutron.
When an atom emits a [tex]{ \beta }^{ - }[/tex] (electron) particle, one of its neutrons releases a [tex]{ \beta }^{ - }[/tex] (electron). And since an electron's charge is negative (-) the neutron loses its negative charge (since neutron's electrical charge is neutral) and turns into a proton.
This is simply explained ^
There are some other details but this should be enough :)
