N5
て（順序）
て（じゅんじょ）
And, And then, After that (sequence)
晩ご飯を食べて歯を磨いた。
I ate dinner and brushed my teeth.
Explanation
The て-form can string together several actions that happen one after another: 「朝起きて、顔を洗って、ご飯を食べる」 (get up, wash your face, eat). It says the first is done, then the next. Tense, politeness and positive or negative for the whole sentence are decided by the last verb; the て-forms in the middle do not change.
Mixed up with
「〜て」 follows the order in which things happen and cannot be reversed; 「〜たり〜たりする」 just gives examples, with no order.
The て-form in the middle cannot carry 「ます」 or 「ない」 in front of it: never 「行きましたて」 or 「食べないて」.