The full details of classical grammars are beyond the scope of this site, but the following basic remarks will prove useful.
All scientific names, regardless of their origin, are treated grammatically as Latin. Most are derived from Latin and its successors or from ancient Greek. The Greek alphabet and words are transliterated in accordance with generally accepted rules which are followed here, except that upsilon (υ) is transliterated as u rather than y. Following tradition, eta (η), the long e, is transliterated as ē, and omega (ω), the long o, is transliterated as ō.
Latin nouns are declined and verbs are conjugated, that is, their terminations change according to their case, tense, person and number, or, more simply, the manner in which they are used. On this site nouns are indicated in the nominative singular (salix willow-tree) and, where the derivation is from the stem of the noun, in the genitive or possessive case also (salicis of the willow-tree). Latin verbs are shown in the present infinitive (salire to leap), rather than the present indicative (salio I leap). Greek verbs are treated slightly differently here, being shown in the present indicative form (bainō I walk), but translated as the present infinitive form "to walk."
Adjectival epithets or trivial names have to agree in gender with that of the genus to which they are assigned. If a species is transferred from a masculine genus to a feminine one, or vice versa, the specific termination must be changed accordingly. Some species names that may look like adjectives are, in fact, nouns in apposition given an adjectival function, and their terminations do not change to agree with the gender of the generic name(e.g. Emberiza cirlus, based on an autochthonym, not Emberiza cirla).
The commonest Latin terminations are:
(1) –us (masculine), –a (feminine), –um (neuter).
(2) –is (masculine), –is (feminine), –e (neuter).
(3) –er (masculine), –era (feminine), –erum (neuter).
The series of papers by David & Gosselin (2000, 2002a, 2002b, 2011, 2013 (Appendix 4 in Dickinson & Remsen (ed.), 2013)) have proved very useful, and will reward careful examination.