What are the rituals of the early church?

Baptism was apparently a part of Christian worship form the earliest times. Baptism as an initiation into a new faith was practiced by the Pharisees when they took converts into Judaism. Jesus' disciples baptized converts even during his ministry, and Paul baptized converts wherever he went. It appears originally to have been an outward sign of the change in status from the pagan life to the Christian life, and later took on deeper meanings.

The second addition of the early Christians was the Eucharist, or communion meal. This was probably modeled on the Seder meal of Judaism, in which the community recalls divine history as they partake of sacred foods. Specifically, it was adopted by Christians from the model of Jesus' last supper with his disciples on the evening before his death

from Religions of the World by Lewis M. Hopfe

Yes, Christianity has two rituals/ordinances:

1. Baptism of believers - Jesus told his disciples to:

Mat 28:19 Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,

2. Breaking of bread/communion - Paul wrote this to the Corinthian Church (he was speaking about Jesus):

1Co 11:23 For I received from the Lord that which I also delivered to you: that the Lord Jesus on the same night in which He was betrayed took bread;

1Co 11:24 and when He had given thanks, He broke it and said, "Take, eat; this is My body which is broken for you; do this in remembrance of Me."

1Co 11:25 In the same manner He also took the cup after supper, saying, "This cup is the new covenant in My blood. This do, as often as you drink it, in remembrance of Me."