Use ～始める when you want to say that someone starts an action that continues over time. It is a compound verb, so the first verb is in its ます-stem form. For example, 雨が降り始めた means 'It started to rain.' This pattern is common and used in both speaking and writing.

Note that ～始める focuses on the starting point of an action, not the process of beginning something like starting a new job. For starting a new activity or project, you use the verb 始める by itself (e.g., 仕事を始める). The compound form is only for actions: 歩き始める, 読み始める, etc.

Also, ～始める can be used with both volitional actions (like reading) and non-volitional events (like raining). It is straightforward and you can use it as soon as you learn the ます-stem form.