Nouns
Latin nouns decline according to five declensions. The principal parts of a noun are its nominative and genitive singular forms, for example:
matella, matellae. nf. chamber pot.
From the genitive ending -ae, the noun matella is identified as a first declension noun. Dropping the genitive ending gives the base matell- to which endings are added.

Some nouns have plural forms only. For these nouns, the principal parts are the nominative and genitive plural forms. For example:
castra, castrorum. nn. camp.

Again the genitive identifies the declension, in this case second declension, as well as the base castr- to which endings are added.

Basic usages of the various cases
Nominative: Subject of a sentence, predicate nominatives
Genitive: Possession or attachment. The genitive case was disappearing from colloquial Latin (the Latin of everyday speech, usually called Vulgar Latin) and was often replaced by the preposition "de" followed by the ablative case.

Dative: Indirect object. Like the genitive case, the dative case was also disappearing from colloquial Latin. The preposition ad followed by the accusative case was sometimes used as a substitute in colloquial Latin.

Accusative: Direct object, object of prepositions of motion towards

Ablative: Means (instrument), object of prepositions of position and of motion away

Locative: Location or position. In Latin, this case is a remnant of the old Indo-European Locative case. It is used primarily with place names and a handful of nouns denoting classes of places like domus (home). For most purposes it has been superseded by the use of the prepositions in or ad followed by the ablative case.

Vocative: Personal address

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Verbs
Here you will find the paradigm of the verb "amare" ("to love"):
amo, amare, amavi, amatus. I love, to love, I (have) loved, loved.
Some verbs are impersonal, i.e., they only exist in the third person singular. (Example: miseret, miserere, miseruit, miseritum. It is a pity, to be a pity, it was a pity, having been a pity.)

Some verbs are intransitive, i.e., they do not take direct objects. The fourth principal part of these verbs is either the neuter form of the perfect passive participle for verbs intransitive verbs which take an indirect object in the dative case, or the future active participle for other intransitive verbs. (Examples: asto, astare, asteti, astatum I assist, to assist, I assisted, assisted. sum, esse, fui, futurus. I am, to be, I was, about to be.) Intransitive verbs which take indirect objects may have impersonal passive voice forms which are occasionally tricky to translate.

Some verbs are deponent which means that they are passive in form but active in meaning. (Example: misereor, misereri, miseritus sum. I pity, to pity, I pitied.)

And finally, some verbs are irregular and their paradigm must be laernt by heart. Example: esse (to be), fieri (to become, to be made), ire (to go), malle (to prefer), velle (to wish).

Conjunctions
Simple conjunctions

ac: and.
at: but. (This is more emphatic than sed.)
atque: and, and also, moreover.
aut: or.
et: and.
nec non: and besides.
sed: but.
vel: or.

Paired conjunctions
atque...atque: both...and.
aut...aut: either...or.
et...et: both...and.
nec...et: not only...but also.
Note: the meaning of the first conjoined expression is affirmative rather than negative not only in Latin but also in English (nec in lingua Latina classica et in lingua Anglisca moderna)!
nec...nec: neither...or.
ut...ita: Although...nevertheless.