They affect population size in 3 ways; positive, negative or neutral. To have a positive affect birth and positive-migration would have to outpace death and negative-migration and inversely if death and negative-migration outpaced birth and positive-migration you would see smaller population.
Many factors can affect all of these but first look at birth. Obviously fertility will affect birth rates in any society but many countries now are facing couples who are just deciding not to have as many children, which effects population. If you have a high birth-rate but low survival rate this may effect pop. size. Death of course means you are no longer part of the pop. even tho they still seem to vote in some states. If a pop. has a great amount of death then the pop will decrease. Fertility, if no1 is able have children then the only way to off-set the deaths is to have positive-migration.
Positive-migration is when people move from one pop. set to another. This can be affected by economy, standard of living, environmental concerns, etc. Negative would be people leaving your pop. set for a different pop. Notice that all those factors can also effect birth,death and fertility.