〜てから
after doing, once … (then)
Verb て-form + から
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て-form + から means "after doing A, (then) B", with the emphasis on the order: 宿題をしてから遊びます, "I'll play after I've done my homework", in other words, not before.
Plain て-form joining (起きて、顔を洗う) just lists actions in order. てから insists the first is finished before the second starts, which is why it's the natural choice for instructions: 手を洗ってから食べてください.
It also marks a starting point in time: 日本に来てから三年です, "it's been three years since I came to Japan".
Careful: past + から (したから) means "because I did". The て-form is what makes it "after".
Examples
宿題をしてから遊びます。
I'll play after I've done my homework.
手を洗ってから食べてください。
Please wash your hands before you eat.
日本に来てから、日本語の勉強を始めました。
I started learning Japanese after I came to Japan.
先に電話をかけてから行きます。
I'll call first, then head over.
晩ご飯を食べてから、テレビを見ました。
After dinner I watched TV.