When you trust a person, you believe that they have your best interest at heart. They wouldn't do something to hurt you for the fun of it, or for selfish gain. You earn a person's trust by consistently proving yourself to them. You show them that you will not use them or take advantage of them. You will not abuse their love or their generosity. You will think of them before acting.
Re-earning a person's trust is done in the same way, except it take a much longer period of time. People are very different as to how easily they'll trust others -- some have been seriously hurt in the past and hesitate to trust again. Others are very "trusting," even of those who don't deserve their trust. No matter the individual, you earn and re-earn people's trusts through reliance on the integrity, strength, ability, surety, etc., of a person or thing; confidence consistency of character -- you prove that you are trustworthy by your deeds.