Words of Greek origin make up some 15% of the English language.
Since the living Greek and English languages were not in direct contact until modern times, borrowings were necessarily indirect, coming either through Latin (through texts or various vernaculars), or from Ancient Greek texts, not the living language. More recently, a huge number of scientific, medical, and technical neologisms have been coined from Greek roots—and often re-borrowed back into Modern Greek.
Still, there are a few Greek words which were borrowed organically—though indirectly. The English word olive comes through the Romance from the Latin word olīva, which in turn comes from the Greek . This must have been an early borrowing, since the Latin v reflects a still-pronounced digamma. The Greek word was in turn apparently borrowed from a pre-Indo-European Mediterranean substrate. A later Greek word, βούτυρον, either borrowed from or calqued on a Scythian word, becomes Latin butyrum and eventually English butter. A larger group of early borrowings, again transmitted first through Latin, then through various vernaculars, comes from Christian language: bishop from episkopos (originally meaning just an 'overseer'), priest from presbyter, and church from kyriakon. Unlike later borrowings, which came from a written, learned tradition, olive, bishop, and so on were transmitted through vernaculars, so their English spelling does not reflect its Greek form.
Until the 16th century, the few Greek words that were absorbed into English came through their Latin derivatives. Most of the early borrowings are for expressions in theology for which there were no English equivalents. In the late 16th century an influx of Greek words were derived directly, in intellectual fields and the new science.
In the 19th and 20th centuries a few learned words and phrases were introduced using a more or less direct transliteration of Ancient Greek (rather than the traditional Latin-based orthography) for instance nous, hoi polloi.
Finally with the growth of tourism, some words, mainly reflecting aspects of current Greek life, have been introduced with orthography reflecting Modern Greek.
The written form of Greek words in English
Greek words borrowed through the literary tradition (not butter and bishop) are often recognizable from their spelling. Already in Latin, there were specific conventions for borrowing Greek. So Greek υ was written as 'y', αι as 'æ', οι as 'œ', φ as 'ph', etc. These conventions (which originally reflected differences in pronunciation) have carried over into English and other languages with historical orthography (like French, but not Italian). They make it possible to recognize words of Greek origin, and give hints as to their pronunciation and inflection.
In some cases, a word's spelling clearly shows its Greek origin. If it includes ph or includes y between consonants, it is very likely Greek. If it includes rrh, phth, or chth, or starts with hy-, ps-, pn-, or chr-, or the rarer pt-, ct-, chth-, rh-, x-, sth-, or bd-, then it is with very few exceptions Greek. One exception is ptarmigan, which is from a Gaelic word, the p having been added by false etymology.
In English, Greek prefixes and suffixes are usually attached to Greek stems, but some have become productive in English, and will combine with other stems, so we now have not only metaphor (good Greek word) and metamathematics (modern word using Greek roots), but also metalinguistic (Greek prefix, Latin stem).
In clusters such as ps- at the start of a word, the usual English pronunciation drops the first consonant; initial x- is pronounced z. Ch is pronounced like k rather than as in "church" (e.g. character, chaos). Consecutive vowels are often pronounced separately rather than forming a single vowel sound or one of them becoming silent (e.g. hierarchy, contrast priest).
Plurals
The plurals of learned Greek-derived words sometimes follow the Greek rules: phenomenon, phenomena; tetrahedron, tetrahedra; crisis, crises; hypothesis, hypotheses; topos, topoi; but often do not: colon, colons not *cola (except for the very rare technical term of rhetoric); pentathlon, pentathlons not *pentathla; demon, demons not *demones. Usage is mixed in some cases: schema, schemas or schemata; lexicon, lexicons or lexica. And there are misleading cases: pentagon comes from Greek pentagonon, so its plural cannot be *pentaga; it is pentagons.
See also
Wiktionary
