Say what happens after something else
後で marks that something happens after an action or a point in time.
JLPTN5
... + 後で~ ato de
after [action or time], ...
After a noun you attach の before 後で — 昼ご飯の後で (after lunch), 授業の後で (after class) — and after a verb you use its past (た) form before 後で. Whatever comes before 後で is the thing that finishes first.
Tips and Common Traps
Hana· Key point
Use 後で to plan your day out loud — 宿題の後で遊ぼう (let's hang out after homework).
Maru· Common trap
The verb before 後で must be in the た (past) form — not the dictionary form. 食べた後で ✓, not 食べる後で.