To get involved in something (often used for getting involved in undesirable or illicit activities).
彼は若いときに反社会的な活動に手を染めてしまった。
When he was young he got involved in antisocial activities.
一度でも不正に手を染めると、後戻りは難しい。
Once you get involved in wrongdoing, it's hard to go back.
好奇心で危ない仕事に手を染めないよう注意した方がいい。
You should be careful not to get involved in dangerous work out of curiosity.