begin(start) doing/to do
begin / start to do sth
begin / start doing sth.
1) 谈及一项长期活动或开始一种习惯时，使用doing.
How old were you when you first started playing the piano?
你几岁时开始弹钢琴?
2) begin, start用进行时时，后面动词用不定式to do
I was beginning to get angry。
我开始生起气来。
3) 在attempt, intend, begin, start 后接know, understand, realize这类动词时，常用不定式to do。
I begin to understand the truth。
我开始明白真相。
4) 物作主语时
It began to melt.
From:https://www.zgghmh.com/CET-4/20001555.asp