I want to know the grammar about the word AFTER
if I want to describe something happens after a particular time, are there only two ways to make a sentence with AFTER?
1) after doing something
2) after someone did something

Question

I want to know the grammar about the word AFTER
if I want to describe something happens after a particular time,  are there only two ways to make a sentence with AFTER?
1) after doing something
2) after someone did something

Answer

Close. There are three main ways of using "after":
a) as a preposition, which would usually precede a noun, a preposition or (as in your "1") a gerund: "I came after the show", "I came after him" or "I came after going to the show".
b) as a conjunction, which connects what would otherwise be an independent clause to the subsequent event (as in your "2"): "I came after I went to the show".
c) As an adverb: "He came first, and I came soon after"

(Also note it should be "describe something WHICH/THAT happens".)
Consequently, your

집에서 편안하게 언어를 배울 수 있는 기회를 놓치지 마세요. 경험 많은 강사진을 살펴보고 지금 바로 첫 수업을 신청하세요!