What does the bible say about the order of worship/church service?
The Bible says nothing about an order of worship. The assemblies of the early church may have been very informal, with some singing, a few people preaching or commenting on the scriptures, and some prayers, in no preset order. 1 Corinthians 14:26 seems to show this.
There are certain things that we know were part of the assemblies. These include singing (Ephesians 5:19, Colossians 3:16), scripture reading and preaching (1 Timothy 4:13, Acts 20:7), and prayer (1 Timothy 2:1-3). Contributing money into the treasury of the church was not uncommon (1 Corinthians 16:1-3; 2 Corinthians 9:6-7). The church also took the Lord's Supper at some times (Acts 20:7 perhaps; 1 Corinthians 11:20-29). Whether it can technically be called "worship" or not, they also met to socialize with one another (Acts 2:42-47).
In general, the assembly of the early church was based on the synagogue assembly of the Jews. That included prayers, singing, scripture reading and discussion, and giving.