With verbs of saying such as "λεγω": ὁτι with the indicative mood and retaining the tense of the original direct speech. e.g. λεγω ὁτι Ἀχιλλευς καλος ἐστι
With verbs of hoping and swearing such as "ἐλπιζω" but also "φημι": the infinitve with the subject of the oratio obliqua in the accusative if different from the subject of the main clause. e.g. φημι τον Ἀχιλλεα καλον εἰναι
With verbs of knowing and percieveing such as "ὁράω": as with 2. but with the participle. ὁράω τον Ἀχιλλεα καλον ὀντα