…be aware that some consider orientate non-standard in U.S. English.
Orient (v) and orientate (v) are all but interchangeable. Even the OED entry for orientate is “=orient”. Both words have a literal meaning: “position or align to face east or, by extension, in any specified direction or relative to some other defined data; or ascertain the bearings of”; and a figurative meaning: “bring into a defined relationship to known facts or principles”. There are also technical meanings which have to do with molecular and sub-molecular alignment. Here are some examples:
History orients us to the present.
In the thick fog, only sounds helped him orientate himself.
They began to orient to their new environment.
Plant leaves and stems orientate themselves towards the light.
If the bee orients her waggle* 90° to the left of vertical… (Mark Ridley, Animal Behaviour)
Pressures on management are orientated towards shareholder rather than employee welfare… (JE Parkinson, Corporate Power and Responsibility)
* So far, my favourite phrase of the week.
The shorter verb dates from 1727; the longer one came later, in 1849, when it was printed in the very same journal that seems to have introduced orientation. Since then, orientate has been used by writers such as Aldous Huxley, Margaret Mead, Tennessee Williams, and Randolph Quirk, but this has not stopped it from being criticised.
Bryan Garner calls it a “needless variant”. Other sources are more disparaging still. But Robert Burchfield, after describing the words’ parallel development towards what became in the late 20C a “competition” and a “contest”, tolerantly concludes that “one can have no fundamental quarrel with anyone who decides to use the longer of the two words”. In other words, it is perfectly standard — at least in British English.

[Image: a bee’s waggle dance, which helps them collectively orient(ate) themselves towards floral cues.]
But as Kenneth G. Wilson writes in the Columbia Guide to Standard American English:
American commentators continue to object to orientate (used more frequently by the British), mainly because orient is shorter but also because the figurative use is outstripping the literal one.
Ernest Gowers anticipated this when, in the revised second edition of Fowler’s Modern English Usage, he wrote that orientate “seems likely to prevail in the common figurative use”, while in The Complete Plain Words he remarked that the figurative use was “passing all reasonable bounds”. The subjects of his scorn — a “client-orientated” service, a “purpose-oriented” building — are of a type that seems even more common today.
Both words are often used — and often interchangeably — as participial adjectives (oriented and orientated). Burchfield cites the OED’s examples of each being preceded by adverbs:
environmentally oriented
psychologically oriented
vertically oriented
politically orientated
and by nouns:
adult-oriented
art-oriented
performance-oriented or -orientated
user-oriented or -orientated
degree-orientated
For a fuller flavour, have a rummage through the British and American corpora.
The antonyms disorient and disorientate date from 1655 and 1704, respectively; again they are virtually synonymous. The OED states that while both can mean “cause (a person) to lose his or her sense of direction; make confused as to what is true or correct”, the longer verb can also mean “turn from the East, give an alignment other than eastern; change or vary the alignment of”.
In most cases, though, this slight differentiation seems likely to be increasingly eroded, if the development of orient and orientate is anything to go by. Some decades ago, Eric Partridge noted in Usage and Abusage that orientate is correct as an intransitive (“to face in a particular direction”), but that orient is preferable in all other senses. It may be too late for such a distinction.