Almost all of us know this hadith: "All the sins of my followers [those sins that are repented from and not repeated] will be forgiven except for those which are disclosed to the people. For example, a person commits a sin at night and Allah conceals is for him, and in the morning he goes to the people and says 'I did such-and-such evil deed." And yet, less well known, Rasoolulah sallalahu alahi wa salaam, Mohammed, also told us "To speak the truth, even if it is against you?" So what does covering your sins really mean?
Covering your sins means not bragging about them, or speaking about them without being asked about them.
But if you are asked? [BTW, no Muslim should seek out the sins of another Muslim unless they have fear for their life, safety, ect, 2 cases where is being allowed the Prophet S.A.W suggested negotiations for marriage and business partnership deals as cases].
In cases where you are asked about past wrongs/sins you ARE to speak the truth about yourself, but offer no more than what you are asked. For instance, a woman asks a man if he committed zinaa before they marry. Many men lie about this, but this brother understood properly that "covering" one's sins does not give us permission to "lie" about them when confronted with questions about them. He told this sister the truth, that he had done haraam in his past but had reformed and never wanted to do such again and was properly ashamed. She forgave him, and they married (after some medical tests to screen for STDs ect). This IS proper Islamic manners. Lying isn't, and never is. I also know of one sister who admitted the same to a good Muslim brother and he forgave her likewise;)
Covering one's sins simply means having the proper shame for them. Don't go out speaking about them, or you make them lighter, you might make them seem "less shameful". The first step towards repentance is having a realization that your actions are wrong and have shame for them. But not to add more sin to yourself by LYING about them. Me, personally, I don't want to have more people standing accusing me on the day of judgement for lies, ect.