How does the indirect statement work in Latin?

Indirect statement denotes indirect speech: not 'He ran' but 'I said that he ran'. The construction that Latin uses is the accusative and infinitive after the introductory verb, and so in the example, 'I said' is the introductory verb, the subject of the indirect statement 'he' is in the accusative rather than the usual nominative, and the verb 'ran' is in the infinitive rather than the usual indicative. There are 6 kinds of infinitive (present, future and past in both the active and passive) and when deciding which to use, it is important to consider what was originally said in the direct speech, and so in the example it would be 'he ran'. This is, therefore, a past active infinitive. Once you've worked out that it is an indirect statement, worked out what becomes the accusative and what becomes the infinitive, you can find the correct forms of the nouns and verbs to finish the sentence.