A compound verb meaning "begin to do" can be formed using the verb hajimeru (begin). Hajimeru is attached as an auxiliary, to a verb in its stem form which indicates that someone or something begins to do something.
Ame ga furihajimashita.
It began to rain.
「Rain began to fall.」
Densha wa yatto ugokihajimeta.
The train began to move.
Jimu wa Michiko to tsukiaihajimeta tokoro da.
Jim just started to date Michiko.
Hope this helps!
°˖ ✧◝(○ ヮ ○)◜✧˖ ° こゆうきあいはら °˖ ✧◝(○ ヮ ○)◜✧˖ °