A church is a building in which Christians hold religious services.
The church has two entrances.
She goes to St Clement's Church, Oxford.
You use church with no determiner, and immediately after a preposition, when you are talking about a religious service in a church. For example, if someone goes to a service in a church, you say that they go to church.
None of the children goes to church regularly.
People had heard what had happened at church.
Will we see you in church tomorrow?
I saw him after church one morning.
A mosque is a building where Muslims hold religious services, and a synagogue is a building where Jewish people hold religious services. When you are talking about a religious service in a mosque or a synagogue, you usually use a preposition followed by a determiner, but sometimes the determiner is omitted.
He goes to the mosque to worship.
We went for morning prayers at the synagogue.
After synagogue, we had lunch together.