It is usually immensely difficult to get a judge to approve a change of legal guardianship, unless it becomes patently obvious it is in the child's interest for such a change to occur, and there is another appropriate guardian willing and able to step in. Depending on the reason for the request, getting a professional psychiatrist or child support officer to support the petition or testify to the unsuitability of your current guardian should increase your chances of having your request approved.
Approach your current legal guardian to see if he is willing to support a change. Although you and your current guardian will still need to find an alternative guardian, his support will be crucial in getting approval from a judge and will make the process immensely easier. When speaking with him, focus on why it is in his interest--- as well as yours --- for such a switch to occur.
Line up possible replacements. Finding someone who is willing and able to serve as your guardian will increase the likelihood a judge is willing to take away custody from your current guardian. The person you find should be someone without major criminal infractions in his history and able to demonstrate he is financially able to serve as your guardian.
Gain support from a professional. Even if your current guardian approves the switch, a judge may recommend another solution (like family counseling) if no psychiatrist or other family counselor is willing to testify it is necessary. The person should be professionally accredited and able to speak with knowledge about the relationship with your guardian.
Go to or contact your local family court and request the appropriate documentation to file a petition for a switch of guardianship. Laws vary by state and municipality, so check with the clerk of your local court as to the specific process for your region.