In order to express that someone was ‘made to do’, or ‘let do’ something, the auxiliary verbs せる and させる will be used. The meaning that せる and させる will convey (when attached to a verb) is called 使役（しえき） (causative, employment, or using) in Japanese.
A common misconception is that せる and させる are standard conjugations of each verb. However, these auxiliary verbs should be thought of as having their own meaning, in a similar way to how たい, ない, だ, です, and other auxiliaries each have their own meanings.
In order to use these grammar structures, remove the る from る-Verbs, and then add させる. For う-Verbs, change the last kana to the あ sound kana from within the same column (except for う, which becomes わ), and then add せる (る becomes ら, む becomes ま, く becomes か, etc.).

• 息子（むすこ）に野菜（やさい）を食（た）べさせる。
  I make my son eat vegetables.
• 友達（ともだち）にトマトを育（そだ）てさせる。
  I make my friend grow tomatoes.
• 忘年会（ぼうねんかい）で先輩（せんぱい）たちが後輩（こうはい）に歌（うた）を歌（うた）わせた。
  At the end of year party, the seniors made the juniors sing a song.
• 友達（ともだち）が私（わたし）の携帯（けいたい）を壊（こわ）したので、新（あたら）しいの を買（か）わせる。
  Since my friend broke my phone, I will make them buy me a new one.

As usual, する and 来（く）る have special conjugation rules. する will be replaced completely be させる (in a similar way to how できる completely replaces する in the ‘potential’ form). 来（く）る will become 来（こ）させる.

• 嫌（いや）な仕事（しごと）は後輩（こうはい）にさせる。
  I let my juniors do the work that I don't want to do.
• 親（おや）に心配（しんぱい）させることしてはいけない。
  You should not do anything that would make your parents worry.
• 夜遅（よるおそ）くに会社（かいしゃ）に来（こ）させるのはよくない。
  It is not good to make people come to the company late at night.
• 犬（いぬ）を呼（よ）んで、こっちに来（こ）させる。
  To call the dog and make it come to you.