There are 2 common mechanisms of electron donation or withdrawal. the first is induction or differences, sometimes subtle, in electronegativity between a group and the carbon to which it is attached; more electronegative withdraws electron density. Most common heteroatoms except for maybe P are inductively withdrawing. H seems to be slightly releasing altho the mechanism is argued. So methyl groups are more electron releasing than other alkyls and sp3 C more than sp2 than sp.
The second method is resonance. atoms with unshared pairs or pi orbitals can donate electron density by effectively donating the unshared pair as sort of a dative bond to a more positive center. This process happens with OH, NH2, OCH3, SH groups and C=C. Notice these are all inductively withdrawing but resonance donating. The resonance effect, that works mostly thru the pi orbital system, is usually more important.
There is also electron withdrawal from resonance. In these cases the group usually has O double bonded to the central atom of the group: C=O, C=O-OH[here the carbonyl withdraws and the OH donates each modifying the other], NO2, CN, SO3H, and similar groups. 
Finally there are the super inductive withdrawers, CF3 and NR3+.
The effects of electron donating and withdrawing substituents in benzyl and phenyl compounds are summarized in the Hammett equation: