Outside of the use of ablatives as adverbial phrases and objects of prepositions. There are a few more ways that the ablative can be used, with or without prepositions. (See declensions here Latin Declensions)
Ablative of Means or Instrument
The ablative of means or instrument is a noun or pronoun that answer the question of “by what means?”, aka “by what?/with what?“. It is written as a noun in the ablative case without a preposition.
Examples: Litterās stilō scrīpsit ; He has written the letter with a stylus. Suīs labōribus urbem cōnservāvit; Through his labors, he has saved the city.
Ablative of Accompaniment and Manner
The ablative of accompaniment and manner is a noun or pronoun in the ablative with the preposition cum. It seeks the answer the question of “with whom or what was the action performed?”
Examples: Cum amīcī vēnērunt; They have come with friends. Id cum virtūte fēcit; He has done it with virtue
Ablative with Cardinal Numerals
When using cardinal numerals, (except mīlia), the item of a fixed amount of the whole is expressed with ex or dē followed by the ablative.
trēs ex amīcīs meīs, three of my friends centum ex virīs, 100 of the men
Ablative of Time When or Within Which
To indicate when or within which period of time an action occurred, the Romans would use the ablative without preposition. In English, we can’t do that, so we supply a preposition when translating.
Eō tempore nōn poteram id facere; At that time (ablative), I was not able to do it. Agricolae bonīs annīs valēbant; The farmers were doing well in the good years(ablative). Paucīs hōrīs id faciet; In a few hours(ablative), he will do it.
Ablative of Personal Agent
The personal agent is used in passive voice constructs to show the agent who performs the action. The ablative of personal agent is constructed by using ā/ab followed by the agent in the ablative case. The ablative of personal agent are used when the action is done by a who. If the action is accomplished by some means, then the ablative of means is used. Below follow some examples:
Dī Caesarem admonent — The gods are warning Caesar Caesar ā dīs admonētur — Caesar is being warned by the gods. (agent, gods are warning) Caesar hīs prōdigiīs admonētur. — Caesar is warned by these omens. (means, how is the warning happening)
In general, agents tend to be beings who can actively do the action, means tend to be things that do the action by nature. Aka: people, animals, gods vs fire, weather, abstract concepts.
Ablatives of Place From Which and Separation
The ablative from which is common construction used to indication the location from where/which the verb of active motion is begun. This construction often uses, ex, ab, or de.
Graecī ā patriā suā ad Italiam nāvigāvērunt. — The Greeks, from their Country, have sailed to Italy. Cicerō hostēs ab urbe mīsit. — Cicero has sent the enemy from the city.
The ablative of separation is used to show that the noun in the ablative is now separated from the other nouns in the sentence.
Agricolae pecūniā saepe carēbant. — The farmers were often lacking in money. Eōs timōre līberāvit — He has freed them of fear.