In Japanese, て is a very important conjunction particle that can be used with many different structures. When it is partnered with a verb, it has special conjugation rules, depending on whether it is being added to a る-Verb or a う-Verb. In the case of う-Verbs, it also depends on what the preceding kana is.

The most common translation in any situation is just 'and' or 'then', due to (B) being highlighted as something that happens/happened after (A).

In these examples, we can see that て basically means '(A) て (B)' = '(A) happened, then (B)'. However, this is only when it is linked to another verb.

Sometimes the て form appears as で. This is a change that happened throughout the course of history, in order to make sentences flow more smoothly. Despite this, there is no difference in meaning between て and で as a vocal change.

The easiest way to identify whether to use て or で is by looking at the preceding kana. If the plain (dictionary) form of the verb finishes in ぐ, ぬ, ぶ, or む, then で will be used. る-Verbs never use で.

ている is a construction used in Japanese to convey that someone or something is existing in a constant state of 'doing' the verb that comes before て. In English, depending on the verb, this can be translated as 'is (A)', 'am (A), or 'are (A)~ing'. The expression is made by adding いる to the て form of either る-Verbs, or う-Verbs.

Due to いる being one of the verbs for 'existing' in Japanese, the ている form means something closer to 'continuing to exist in a specific state', rather than (A)~ing in English. This is why verbs like 死(し)ぬ, and 知(し)る, appear as the ている form in Japanese, when they would appear as the past form in English.