begin 后面跟doing sth.还是to do sth.说明情况

begin to do something 和beging doing something都有表示"开始干什么事情"的意思, 但是有不同

begin doing something特别指很强烈的持续性.比如:

He began smoking three years ago(他三年前开始抽烟)既开始养成习惯

This year the rainy season came earlier than before, it began raining in June(今年的雨季比以前来的早,在六月就下雨了)

begin to do something 表示一件事情的开端,持续与否不重用. 比如:
It's beginning to rain, we had better hurry home(下雨了,我们快回家吧)

At first it was only drizzling, but soon it began to rain heavily(开头只下毛毛雨,可是不久就大起来啦),这里不宜说but soon it began raining heavily.