The process of examination is different for everyone. There are some tried and true methods like solitude and spiritual journaling which are always effective if we apply ourselves to these disciplines. I think its important to set goals and know what your objective is before taking on specific times of spiritual examination. One example would be to set aside 15 minutes each day for one month and spend that time alone with the Lord asking him to examine your heart and mind. Ask him to show you what he thinks this process entails, ask him to help you understand the process, ask him to help you focus and concentrate on this process. If you need to, write these questions and others down to use in your prayer time. It may be good to combine journaling with this time so you can write down what the Holy Spirit is teaching you along the way. The main objective for the first time is to just get started. Trust that the Lord will show you a few things about yourself during this month. You should end the month with a few smart goals based on something the Lord has shown you. It can just be one thing, the quantity is not as important as the followup. Learning to take what God has shown you and work it into your life or correct some aspects of your life is often difficult. I would suggest leaving yourself some space between these focused times of examination. Maybe take a few months break then do another examination month. The goal here is to work at the process of hearing and doing again and again until it becomes second nature.
As you go, its also a good idea to confess any sins when the Holy Spirit brings them up in your mind. Be open to this and let the Spirit do his cleansing work. Hold loosely to anything you identify with or some aspect of your life that you don't want to give up. At least have open ears to hear what the Lord will tell you about that part of your life. We often abort God's plans before they even begin because we let our fear get in the way. Know that God only has good plans in store for us. There may be some pain and suffering along the way, but ultimately He intends good for his children. This process will teach you to trust the Lord and have a relational conversation with the Lord as you pray.