Pre-ます-Form VERB + 始める as “start VERBing”
The verb 始める can be used in conjunction with another VERB in its Pre-ます-Form to form a compound verb that means to “start VERBING.” Although 始める is a transitive verb (its intransitive counterpart is 始まる), the resulting compound verb becomes intransitive or stays transitive depending on the VERB that is used in conjunction (the first verb determines whether the resulting compound verb is intransitive or transitive and 始める is always the second verb in the form Pre-ます-Form VERB + 始める so it always conforms to the other verb used). Given this, 始める is commonly used with both intransitive and transitive verbs in this grammar construct.
Ima shukudai o shihajimemasu.
(I will start doing my homework right now.)
Gym de undou shi hajimemashita.
(I started exercising at the gym.)
Kono anime o mihajimete kudasai.
(Please start watching this anime series.)