Root
The root is the basic core of a word which gives it its main meaning. A root is the only part of a word that can stand alone, e.g.
cpst, dentin, organ.
Usually, though, a root needs to be combined with at least a suffix to complete its meaning, e.g. hepat-, onych-, ventri-.
Some roots have more than one form, e.g. cheir, chir-; hem-, hemat-.
Note that the alternate form is not optional. Some words use one, some another for a variety of reasons, e.g. hemophilia, never hematophilia.
Some roots can occur in a form which cannot begin a word but must be preceded either by another root or by a prefix, e.g. -em- (hem-), -fic- (fac-).
It is possible to have more than one root in a word, e.g. gastroenteritis, palatopharyngoplasty.
There are some roots which have the same meaning but are different roots, not alternate forms, e.g. nephr- & ren- = "kidney"; myx- & muc- = "mucus". Again, the root you use to form any given word is not simply a matter of choice.
 

Suffix
The main job of a true suffix is to indicate what part of speech a word is, i.e. noun, adjective, or verb; it does not have any meaning of its own. It is always attached to a root and when listed alone must be preceded by a hyphen, e.g. -acious (adjective), -ia (noun). Most of the suffixes you will learn in this course are "compound suffixes" or "suffix forms". i.e. they are compounded of a root (sometimes with a prefix), and a true suffix but are used in combination at the end of words so often that they are learned as suffixes. These "suffixes" have a definite meaning, e.g. -pathy (disease), -ectomy (excision), -rrhea (discharge). Some suffix forms can stand as independent words, e.g. phobia (fear), stenosis (narrowing), ptosis (prolapse).
In English, many words which were originally one part of speech can be used as another, e.g. often words with an adjectival suffix, will be used as nouns, antiseptic, clinic.
 

Combining vowels
Generally, if a root and a suffix can combine without any additional letters they will do so, e.g. arthr/itis, nephr/ectomy. However, if a root ending in a consonant is combined with a suffix beginning with a consonant, a vowel (usually o, sometimes i, rarely a,e or u) is inserted to make the word pronounceable, e.g. arthr/o/desis, nephr/ o/ lysis.
Combining vowels are often inserted between roots even when they are not needed for pronunciation purposes, e.g. arthr/o/endoscopy, nephr/ o/ abdominal.
The vowel is considered to have been added to the root. Together they are properly called a combining form.
 

Prefix
A prefix is placed before a root to add to or alter its meaning. When listed by itself a prefix must be followed by a hyphen, e.g. pre-, dys-. Prefixes are generally adverbs and prepositions in origin and carry meaning of their own, e.g. syn- = "together".
Prefixes are never joined to roots with a combining vowel. Most prefixes end in a vowel so there is rarely a problem with pronunciation. If a prefix is joined to a root which begins with the same vowel a hyphen may be inserted, e.g. anti-icteric, or the vowels assimilate, e.g. diarthosis. In those prefixes which do end in a consonant, the final letter assimilates partially or wholly to the initial consonant of a root, e.g. syn- becomes sym- in symmetry and sympathy.
 

Order of components in building and defining a word
Begin your definition with the suffix to get the part of speech correct. Defining an adjective as a noun (or vice versa) is wrong, e.g. cardiac = "pertaining to the heart", not "heart".
The first few words of an English description of a condition will often be the suffix in the medical term, e.g. "a fungal condition of the nails" = onycho mycosis; "surgical puncture of the larynx" = laryngocentesis. Once the suffix is taken care of the order of the roots and English words are generally the same, e.g. cardiopneumopexy = "the fixation of the heart and lungs". Sometimes the connection between the various roots within a medical term cannot simply be expressed by "and". As with any language, when you are "translating" a word you must be sure what you have written makes sense, e.g. cardiomyopexy = "the fixation of the heart and its muscles", not simply "the fixation of the heart and muscles". Prefixes should be taken where they make the best sense, e.g. dysesthesia = "condition of disordered sensation"; hemidysesthesia = "condition of disordered sensation on one side of the body".
 

Synthesizing and analyzing the components of medical terms are not mechanical processes. As with any language you must think about the best way to express the concept of the word in English.