Dopamine's major site of action seems to be in the brain. It is synthesised by the neurons there and is used principally as a neurotransmitter - to signal to other neurons.
Dopamine is formed from the amino acid tyrosine, which you get from a normal diet. [Details at the end.] In the neurons it is stored in vesicles, which are basically each a pool of dopamine surrounded by a membrane. When stimulated to secrete dopamine, the vesicle's membrane fuses with the cell membrane, and the the dopamine is released. It is released into the synaptic cleft (the signalling space between two neurons) where it binds to the receiver cell's dopamine receptors to complete the signal.
As a neurotransmitter it has a role in motivation and reward, learning, motor function (a lack in one region causes Parkinson's), and attention. Also in the brain, it inhibits the release of a milk-producing hormone from the pituitary (prolactin). Therefore, if we want to stop a woman breastfeeding (let your imaginations run wild), we can give her a form of dopamine.
Lastly, some dopamine is also produced by the central region of the adrenal gland (adrenal medulla), probably as a precursor to making adrenaline (epinephrine) and noradrenaline (norepinephrine), which are derived from it.
Hope that helps!
Details (enzyme in brackets):
1. Tyrosine --(tyrosine hydroylase)--> Dopa
2. Dopa --(dopa decarboxylase)--> Dopamine