A field of interest becomes a science once it attempts to study nature and make falsifiable claims. Psychology, for the most part, is indeed a science, as it makes claims about the mind and brain and performs studies (usually behavioral) that are falsifiable in some way.
Psychologist says "I believe that short-term memory is decreased in people who have experienced a recent death in the immediate family" and does memory tests on people who have experienced a recent (a quantified term) death in the immediate (another quantified term) family accordingly, to see if the hypothesis is correct. Once a correlation is made, reasons are hypothesized, and more tests are done. The claim is completely falsifiable though; if it weren't true, there would be no correlation observed in the studies done.
Freudian psychology, on the other hand, is one realm of psychology that is just total garbage. He set the grounds for an interesting theory with the whole subconscious thing, but the field as a whole is pretty non-falsifiable because you can't really find evidence that proves or disproves that we are all just run by our primitive urges. You can attribute any and every action to "primitive urges", but you can't really prove either way if these urges are the actual causes, making it non-falsifiable and ultimately just an interesting belief.
On a side note, typology is the same way, making it a pseudoscience as well.