Our church just finished a week of prayer and fasting which was a wonderful success. How do we know we have succeeded in a time of prayer when prayers operate in the invisible realm of the Spirit?

It's not really that difficult. First of all, we had an excellent percentage of our church involved in each of the two prayer meetings held every day that week.
Next, the people had a mind and heart to really be involved in the praying.
And last, there was a sense among the congregation that there was much accomplished.

You see, we can't always know exactly what has happened as a result of our prayers. But we have the promise of God that if we ask it shall be given, if we seek we shall find, and if we knock it shall be opened.(Matthew 7:7)

God's promises cannot fail. This is assured. But people can fail to gather for prayer, they can fail to fast, they can fail to pray sincere and fervent prayers.
I have preached on prayer in many churches, and the pastor usually shares with me that his greatest problem is getting the church to gather to pray.

I believe this difficulty arises primarily from unbelief. Those in a church who have the firm conviction that prayer changes things, and that prayer is the privilege and responsibility of believers, these are the ones who respond to the call to prayer.

There are many ways to build churches -- marketing, image, compromise, influence, money. But the Biblical way to build a church is on our knees. Actually, we don't "build the church" -- that is Jesus' job. (Matthew 16:18)
But, through prayer, we allow the Holy Spirit to lead us and instruct us how it should be built.

As I am now finishing a new book on prayer I have had opportunity to be reminded of how our ministry, Shekinah Church, was built through a series of miracles.
Beginning with six families taking the responsibility to buy 100 acres of property (and then develop it as the church grew), I am amazed myself how we prayed ourselves into a place of faith to attempt these things.
But our church has been saturated with prayer from day one.

Prayer opened the way to the vision for our ministry. Prayer brought miracles that built the ministry. Prayer
has sustained us through every difficulty. Thanks to God for the privilege and power of prayer.