I would like to know where the custom of praying in church came from. As I try and find it in the Bible, it says that we are not to pray publicly, but we are to go to our closets and pray in private. Can you help me with this?

You question is an excellent one. I think I can help you with scripture for public pray and also answer your question about the emphasis Christ made on praying in secret. Prayer is certainly changed according to who is praying and who is listening to the prayer. Though there seem to be many variations, I find it helpful to divide the kinds of prayer into three: private, public, and participatory or mutual. We will look at each kind of prayer.

PRIVATE PRAYER:

The most important and the most earnest kind of prayer is that which is done privately. You mention the emphasis Christ made on secret prayer. In Matthew 6:6But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
See All..., Christ states, "But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly." This certainly shows us the importance of private prayer.

However, Christ is also dealing with a particular practice of the Pharisees. They made a big show of praying so that everyone would know just how spiritual they were. They were proud and ostentatious in their prayers so that others would see them. That is, they took what should have been their private prayer life and made a public show of it so that others would be amazed at their spirituality. This is akin today to those who continually brag on how much time they spend in prayer. Christ was teaching us that our personal prayer life is not to be displayed in public. He was not teaching that there was never an occasion for public prayer.

PUBLIC PRAYER:

Public prayer is common in the Old Testament. Solomon prayed at the dedication of the temple (1Kings 8:22-23 [22] And Solomon stood before the altar of the LORD in the presence of all the congregation of Israel, and spread forth his hands toward heaven: [23] And he said, LORD God of Israel, there is no God like thee, in heaven above, or on earth beneath, who keepest covenant and mercy with thy servants that walk before thee with all their heart:
See All...). Elijah prayed publicly on Mt. Carmel (1Kings 17:36-37
See All...). Ezra prayed before "a very great congregation of men and women and children" (Ezra 10:1Now when Ezra had prayed, and when he had confessed, weeping and casting himself down before the house of God, there assembled unto him out of Israel a very great congregation of men and women and children: for the people wept very sore.
See All...). If public prayer is not allowed in the New Testament, it is definitely a change in what God allows.

However, we continue to see public prayer practiced in the New Testament even after the teaching of Matthew 6:6But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
See All.... Christ prayed publicly before He raised Lazarus from the dead (John 11:41-42 [41] Then they took away the stone from the place where the dead was laid. And Jesus lifted up his eyes, and said, Father, I thank thee that thou hast heard me. [42] And I knew that thou hearest me always: but because of the people which stand by I said it, that they may believe that thou hast sent me.
See All...) as well as on other occasions. Paul kneeled and prayed with the Ephesian elders before he left them (Acts 20:36And when he had thus spoken, he kneeled down, and prayed with them all.
See All...). And although we receive few clear statements about the order of worship in the early churches, an important piece of information is found in 1Corinthians 14:15-16 [15] What is it then? I will pray with the spirit, and I will pray with the understanding also: I will sing with the spirit, and I will sing with the understanding also. [16] Else when thou shalt bless with the spirit, how shall he that occupieth the room of the unlearned say Amen at thy giving of thanks, seeing he understandeth not what thou sayest?
See All..., which states:

1Corinthians 14:15-16 [15] What is it then? I will pray with the spirit, and I will pray with the understanding also: I will sing with the spirit, and I will sing with the understanding also. [16] Else when thou shalt bless with the spirit, how shall he that occupieth the room of the unlearned say Amen at thy giving of thanks, seeing he understandeth not what thou sayest?
See All... What is it then? I will pray with the spirit, and I will pray with the understanding also: I will sing with the spirit, and I will sing with the understanding also. Else when thou shalt bless with the spirit, how shall he that occupieth the room of the unlearned say Amen at thy giving of thanks, seeing he understandeth not what thou sayest?

If you carefully read this passage, you will see that Paul stresses the importance of praying with understanding so that those who occupy the room of the unlearned can say Amen at the giving of thanks. This passage makes sense only in the context of public prayer. If no one is listening, then how could anyone say Amen? Other statements hint at the presence of public prayer in the early churches, but this one clearly shows that it was practiced.

One thing that might help you is to understand that the purposes of public prayer are a bit different from those of private prayer. In private prayer, we pour our heart out to God and tell Him all. We do not need to be concerned about sentence structure or form in any way. Just talk to God. However, in public prayer, we are leading (as we speak of someone "leading in prayer"); we are leading others to look on God. We are directing the attention of others to the Lord and helping them rely on Him at this time. Again, the sin of Matthew 6:6But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
See All... was to make a public display of private prayer. It is not dealing with the proper use of public prayer (though public prayer can be misused as a display too).

PARTICIPATORY PRAYER:

This could also be called mutual prayer. It refers to times when more than one person participate in prayer together. In one sense, it is public. But instead of one person praying and others saying Amen to their prayers, it involves a group of people joining together in prayer. Yet, there seem to be varying degrees of this. On one end of the spectrum, Jesus took three of His disciples with Him to pray in the Garden of Gethsemane. After the disciples fell asleep, Christ scolded Peter, "What, could ye not watch with me one hour?" (Matthew 26:40And he cometh unto the disciples, and findeth them asleep, and saith unto Peter, What, could ye not watch with me one hour?
See All...). Jesus was going to pray a little distance from them, but they were to watch with Him in prayer. In a sense, they were to participate in His private prayer. On the other end, on one occasion the apostles lift up their voice to God with one accord (Acts 4:24-30 [24] And when they heard that, they lifted up their voice to God with one accord, and said, Lord, thou art God, which hast made heaven, and earth, and the sea, and all that in them is: [25] Who by the mouth of thy servant David hast said, Why did the heathen rage, and the people imagine vain things? [26] The kings of the earth stood up, and the rulers were gathered together against the Lord, and against his Christ. [27] For of a truth against thy holy child Jesus, whom thou hast anointed, both Herod, and Pontius Pilate, with the Gentiles, and the people of Israel, were gathered together, [28] For to do whatsoever thy hand and thy counsel determined before to be done. [29] And now, Lord, behold their threatenings: and grant unto thy servants, that with all boldness they may speak thy word, [30] By stretching forth thine hand to heal; and that signs and wonders may be done by the name of thy holy child Jesus.
See All...). It is almost as if they prayed the same thing in unison.

However, there must have been many variations of this. In Acts 12:5Peter therefore was kept in prison: but prayer was made without ceasing of the church unto God for him.
See All..., Peter was thrown into prison, "but prayer was made without ceasing of the church unto God for him." When he is released, he goes to the house of Mary the mother of John Mark, "where many were gathered together praying" (Acts 12:12And when he had considered the thing, he came to the house of Mary the mother of John, whose surname was Mark; where many were gathered together praying.
See All...). This is not private prayer, but neither is it many people listening to one person praying and saying Amen. I believe it was one of the keys of the power of the early churches.

There are other evidences of this participatory prayer in the New Testament. The early disciples met in the upper room and "continued with one accord in prayer and supplication" (Acts 1:14These all continued with one accord in prayer and supplication, with the women, and Mary the mother of Jesus, and with his brethren.
See All...). Paul pleaded with the Romans, "that ye strive together with me in your prayers to God for me" (Romans 15:30Now I beseech you, brethren, for the Lord Jesus Christ's sake, and for the love of the Spirit, that ye strive together with me in your prayers to God for me;
See All...). The Corinthians are expected to be "helping together by prayer for us" (2Corinthians 1:11Ye also helping together by prayer for us, that for the gift bestowed upon us by the means of many persons thanks may be given by many on our behalf.
See All...). Taken together, it is certain that the early churches gathered together for mutual prayer in which all participated. We should be doing the same today.

In conclusion, prayer takes many forms. Our truest prayer is to be found in our private times with God. This prayer should be done in the closet and in secret. It is not for display. However, there are proper times for one person leading in public prayer and there are also proper times for God's people to prayer together. Each kind of prayer can find its God-given place in our service to Him.