Lying to authority figures is something I have gotten good at over the years. These steps are what I do to keep out of trouble. This is going to take some practice before you get it right for yourself. This isn't something you can learn overnight, but if you get good at it, it will save your neck in the end.
Step 1: Stay Calm
Remember, you're innocent even if you're not. You have nothing to worry about.
It helps to convince yourself that you are telling the truth to begin with. You can not be lying if you don't think you're lying. You might be delusional, but that doesn't matter since you have convinced yourself you are telling the truth.
Step 2: Speak in Generalities
This sometimes works if the person is stupid enough. If your person is good at interrogation this is only going to make them angry. Trust me.
It's good to offer as few details as possible. Only give details if asked for them. Details can be used to unravel lies.
Step 3: Be Prepared
Think of it like a test or a job interview. Think before hand of the questions that this person might ask and rehearse the answers to yourself. Remember to keep the answers short and to the point. Don't provide needless details or bad alibis.
Step 4: Keep Eye Contact and Positive Body Language
There are certain tells that can give away that someone is lying. For instance, when my dad lies he gets all bug-eyed. In fact, many people do that.
To keep from giving yourself away the first thing you want to do is keep eye contact with the person you are talking to. Unless, you are one of those freaks that never make eye contact with anyone. Then, whatever you do, don't make eye contact.
The best way to make eye contact is to focus on an imaginary spot somewhere to the left of their head around their left ear. This will seem like you are looking straight at them.
Keep a neutral and relaxed posture and don't do anything that would make you seem nervous like shake or scratch your neck. I like to stay relaxed by singing Irish folk songs to myself. The kind of song that goes on and on and on.
Step 5: Live Your Lie
If you are going to lie, you have to stand behind it from then on and never change your story. Bring it up from time to time when talking to the person. It will seem more truthful.
Step 6: Don't Get Caught
If you get caught, never tell the truth. Make up another lie or tell a half-truth that isn't as bad and would have forced you to make up the original lie. The goal is to distract them from the real truth and keep yourself out of trouble.