Well that was a long day. My mother in law is out of state on a vacation and we're refinishing the floors in her house for her birthday. We moved everything back in today.
The first thing in prayer is to go before God, with praise and thanksgiving and acknowledging the sacrifice of His Son as the only way we have the privilege to do so. God created us to love and be loved, both ways, so enter His presence (and conversely welcome His presence around you) with love and appreciation and acknowledgment. Invite the Holy Spirit to surround you, to wash thru not just you but your environment, to cleanse it of the enemy that would try to interfere. Invite angels to occupy the enemy, and to bear you up in prayer. You need to form, pardon the expression, something like a warp bubble around you, both spiritually and physically, where you're in God's presence and God's presence surrounds you.
Confession is next. You have to understand the power of sin. Forgiveness for salvation is a once-for-lifetime event, and the power of sin has no effect on it. God will keep you for as long as you will stay, and regard you as pure no matter how dirty you get.But the power of sin in the here and now is that if you submit to a spiritual authority, you're submitted to a spiritual authority... until you rebuke it. When you submit to either a demon and/or the flesh yanking on your leash, you empower it over you. Confession is the way you rebuke that. Bring it before God, confess what you got dirty in, and pray the Blood of Christ be poured out upon and within you for the cleansing it brings in both spirit and body. And pray the Holy Spirit be poured out upon you as well, filling your spirit to be stronger against the flesh. And ask that angels be set around you, to bear you up and to occupy the enemy. And wield your sword – the word of God – on your lips.
Then tell Him why you are there. Lay the situation out (as you know it) before Him, knowing that He already knows more about it, and has a plan. He does already know about it, but there's a partnership clause in the contract that usually, but not always, has to come into play. So He knows about it, we come to Him and say can we do something about it, and in honor of your faith He will.
With that partnership established, face the demons themselves and tell them what for. You have the authority to command their silence; you have the authority to command them bound. Well, not you, but Christ has the authority, much like the Sheriff, but it is we who enforce it as His deputies. So you bind them and book 'em, and tell them if they have any issues with it to take it up with the Judge.
Casting them out is a different issue. Most will flee if you show them the Door, but some will take fasting with those prayers to break the hold of. This is where praying in a group is helpful, God says where two or more agree it will be done, and that includes tossing out the tough guys. Hey, they fight in groups so why shouldn't we?
Now, if you are praying for someone else, repeat all those steps above over them. Names in the spiritual denote place and position, you can speak the name of Jesus over the name of the person you are praying for as a covering over them.
Then lay it all before God in faith, tell Him here it is it's Yours, thank Him and praise Him for the privilege of being able to lay it before Him, and for He will do with it. Acknowledge again the sacrifice if Christ as the Authority that enables you to do all these things, invite Jesus to be Lord over these things, and say amen.