The subject of every sentence will be in the nominative case.
A finite verb agrees with its subject in number and person.
A neuter, plural, nominative often takes a singular verb. cf. BBG 9.16.
παντα (pl)δι αυτου εγενετο (sg)
ταυτα (pl)εν βηθανια εγενετο (sg)περαν του Ιορδανου.
A predicate nominative is always in the nominative case.
An object is in the accusative case (but see principle 47).
Adjectives, possessive pronouns, participles, and the article always agree with whatever they are modifying in gender, number, and case.
An articular participle will always be either attributive or substantival; see BBG 29.5.
A predicate nominative must agree with the noun it modifies in gender, number, and case.
και αυτη εστιν η μαρτυρια
ουτος εστιν ο υιος του θεου
μαρτυρια agrees with αυτη; υιος agrees with ουτος.
A predicate nominative will usually be anarthrous. When it is articular, an essential identity with the subject is asserted.
και ο λογος σαρξ εγενετο
εγω ειμι ο Χριστος
See more detail in GGBB page 40.
An attributive adjective may follow or precede the noun it modifies but in either case the adjective must be articular; cf BBG 9.12.
The last vowel of the stem of many verbs will lengthen when it comes into contact with the tense formative (BBG 19.12). Alpha and epsilon both become eta; omicron becomes omega.
αγαπαω – present tense
αγαπησω – future tense.
Note the tense formative caused the α to become η.
The article will often stand without a noun (an “orphan article”). In such cases, it takes on the nature of a pronoun and always implies some person or persons previously mentioned.
στραφεὶς δὲ ὁ Ἰησοῦς καὶ θεασάμενος αὐτοὺς ἀκολουθοῦντας λέγει αὐτοῖς· τί ζητεῖτε;
οἱ δὲ εἶπαν αὐτῷ ῥαββί, ὃ λέγεται μεθερμηνευόμενον διδάσκαλε, ποῦ μένεις; (John 1:38)
Notice there is no noun that corresponds to οι. This word then becomes “they” and its antecedent is John’s two disciples (John 1:37).
The conjunctions ινα and εαν are usually followed by a verb in the subjunctive mood. Notice μαρτυρήσῃ and πιστεύσωσιν and the conjunctions which precede them:
οὗτος ἦλθεν εἰς μαρτυρίαν ἵνα μαρτυρήσῃ περὶ τοῦ φωτός, ἵνα πάντες πιστεύσωσιν δι’ αὐτοῦ.
Verbs which involve an action of the five senses or of the mind often take a genitive object (GGBB p. 131).
τὰ πρόβατα τὰ ἐμὰ τῆς φωνῆς μου ἀκούουσιν, καγὼ γινώσκω αὐτὰ καὶ ἀκολουθοῦσιν μοι…
Note that φωνῆς (genitive, singular) is the object of the verb ἀκούουσιν.
Likewise, some verbs take their object in the dative case (GGBB p. 171).