The process of deliverance often consists of three main parts: Tearing down strongholds, removing legal rights and then casting out the remaining demons. If you try to cast out demons without taking away the strongholds or legal rights that they are holding onto, then you can't really expect to achieve a complete successful deliverance. Removing these two blockages is vital in going about a complete and successful deliverance.
There is a teaching specifically on Legal Rights too that you may want to go through as well.
What is a stronghold?
A stronghold is a faulty thinking pattern based on lies and deception. Deception is one of the primary weapons of the devil, because it is the building blocks for a stronghold. What strongholds can do is cause us to think in ways which block us from God's best. For example, if you think you have to confess all your sins to everybody you've ever wronged, you'll feel just awful and guilty until you do all that, and even then, you'll probably feel guilty, because you probably forgot many people that you didn't confess your sins to. All unnecessary, and a waste of time, all because you were deceived and thought that you had to do something that you really didn't have to do.
An example of a stronghold at work: A common scene is somebody who is scared of God, and has a hard time feeling His love and presence. They view Him as a cruel taskmaster, and not as the God that is really is to them, and therefore, they put up there own wall which makes it hard for them to receive God's love, presence and draw close in their relationship with Him. If you saw your spouse as a rude and cruel dictator, you probably wouldn't be as apt to snuggle upto Him and love him as you would if you saw him as a loving and kind person who loves you and cares for you. If you see somebody as mean, it's hard to receive their love, isn't it? That's how our perception of God can hinder us from feeling His love and presence in our lives. It is VERY important to have a correct perception of God if we want to live victorious lives in Christ Jesus!
Two very destructive and common strongholds
The first one, where you see God incorrectly: One of the most popular and devastating strongholds to have, is an incorrect image in your mind of who God is, and how He sees us. People who see God as a taskmaster, live their lives with an unhealthy fear of God. There's a good kind of fear of God, which is more like a holy respect for Him, but there's another kind of fear that is very unhealthy that the enemy wants us to have, and it's the kind of fear where we see God as a taskmaster, cruel, cold, distant, uncaring and would snap the whip at us the moment we step out of line. People who are afraid they've committed the unpardonable sin are almost guaranteed to have this stronghold. People who find it hard to feel God's love and presence, often have this stronghold too. If you feel God is distant and cold, or question if God loves you, then you need to get this stronghold torn down.
One awesome book that will help you break down this stronghold is Blessed Beyond Measure by Gloria Copeland. It talks about the goodness of God, and it's impossible to read that book and be the same person when your done seeing the love and goodness that God wants to bless us with!
The second one, where you see yourself incorrectly: People who suffer from this have a hard time seeing the new person that they are now in Christ Jesus, and often suffer from low self-esteem. They don't understand what Christ did for them, and how it applies to their own life. Common symptoms of this stronghold are guilt feelings (questioning if you've really been forgiven of your sin(s)), low spiritual esteem (they feel like sinners, not saints), they lack spiritual confidence that we are supposed to have in Christ Jesus, they may still struggle with sin (Jesus said that if you keep in His Word, which tears down strongholds, you will be free from the power sin has over you - John 8:31-34), and overall you don't feel 'worthy' spiritually and lack the joy of the Lord in your life. If you even remotely struggle with this stronghold, the teaching Forgiven sinner or saint? is an absolute must-read!
One of the best books I've seen for tearing down this stronghold is Victory over Darkness by Neil T. Anderson. It will teach you of the new person you are now in Christ Jesus, and help you be victorious over the darkness through an understanding of your identity in Christ.
I mention common other strongholds over on the Three Stages of Bondage teaching.
How to tear down a stronghold
2 Corinthians 10:4, "For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds."
Strongholds are birthed and dwell in deception (which are lies and false beliefs), so naturally the cure is to bring the truth in God's Word on the scene. You debunk the lies of the enemy, with the truth, which is in the Word of God! The Bible says that our weapons are mighty for the tearing down of strongholds (2 Cor 10:4, "For the weapons of our warfare are not carnal, but mighty through God to the pulling down of strong holds."). What is our primary offensive weapon? The sword of the Spirit, which is the Word of God (Eph 6:17, "...the sword of the Spirit, which is the word of God."). Truth dispels deception and lies, and therefore the more truth you bring into a situation, the more the darkness must flee. This is where it's important to grow in God's Word, is because it is your primary weapon for tearing down the strongholds of deception that the enemy has been feeding you.
In John 8:31-36, Jesus tells us that we can be held in bondage due to strongholds in our lives. And His solution was to, "continue in my word... and ye shall know the truth, and the truth shall make you free." (v. 32-32) Strongholds are torn down as we meditate on God's Word, which is truth!
A great list of Bible verses you can meditate on, which will help you tear down strongholds in your life can be found on the anti-stronghold Bible verses page: http://www.greatbiblestudy.com/bible_verses.php
Another great list of anti-stronghold confessions can be found in the Blessing Confessions list.