This is a very common question that has a surprising answer. Self confidence is not a feeling, at least at first. People who are self confident behave in a pattern that leads them towards the feeling of self confidence. They did not feel self confident, until a pattern of successes emerge. Once the feeling arrived, their behaviors began to be combined with confident thought and feeling.
So how do you get this feeling for yourself?
There is little difference between acting confident and feeling it. This led psychologists like George Kelley to give clients with poor self esteem and lack of confidence assignments as a part of therapy. He believed that your feelings are set on a scale ranging in extremes from one point to another. For example, if you are not self confident, you are on one end of the scale. But in your mind, there are people who are in the confident range of this scale. The secret is to act "as if" you are in the range that you wish to be.
Before you being this process, you have to ask yourself what behaviors would show to you that you are self confident. What behaviors show that you are not self confident? For one week, act as if you are confident and take on behaviors that a confident person would have. At first you will feel like a total fraud. But as the week progresses you will find that your thoughts are pulled toward your behaviors and that you will begin to feel different than you do right now.
I am sure it is true that you are talented and filled with potential. No doubt somewhere in your development you were encouraged to see yourself on the less than self confident end of the scale. As you behaved this way, your thoughts fell in line with the behavior and now you wonder how you could ever feel different. What I am asking you to do in the above suggestion drags the process backwards. It often seems too simple, too easy or too impractical to work. But it does. So, instead of evaluating your developmental past and spending time working through your childhood, let's go right to the point and reverse engineer, you.
Write down a list of confident behaviors. If it helps, identify a couple of confident people you know and list their characteristics. Act as if you are them. You will not exist this week. You, as you are now, will need to cease to exist. If it seems like pretend, it is. But this is how we form ourselves. To pretend we are an identity until we adapt one that fits.
I hope this helps,