You can pray for yourself the very same way you would pray for another. You can even lay hands on yourself. Just rebuke the sickness and ask God to send his Holy Spirit to come and heal you. James 5:14-15 says,
Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord. And the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven.
It seems from this verse that the best way is to solicit prayers from others, especially those who are mature, when you are sick. But there is absolutely no reason why you should not pray for God to heal you when you are sick.
In the same way that you would want to pray with faith, in Jesus’ name, according to God’s will when you pray for someone else, you will want to pray that way for yourself. Remember that sickness and disease is not a part of the perfection of creation, but rather a product of the fallenness of the world in sin. When the Kingdom of God fully comes, you will never be sick. Pray for yourself that in your own body, his Kingdom would come, his will would be done, on earth as in heaven.