Baptism and the Celebration of the Eucharist as described by Didache 50-160 AD (CE)

Chapter 7. Concerning Baptism. And concerning baptism, baptize this way: Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit, in living water. But if you have no living water, baptize into other water; and if you cannot do so in cold water, do so in warm. But if you have neither, pour out water three times upon the head into the name of Father and Son and Holy Spirit. But before the baptism let the baptizer fast, and the baptized, and whoever else can; but you shall order the baptized to fast one or two days before. 

Chapter 8. Fasting and Prayer (the Lord's Prayer). But let not your fasts be with the hypocrites, for they fast on the second and fifth day of the week. Rather, fast on the fourth day and the Preparation (Friday). Do not pray like the hypocrites, but rather as the Lord commanded in His Gospel, like this: 

Our Father who art in heaven, hallowed be Thy name. Thy kingdom come. Thy will be done on earth, as it is in heaven. Give us today our daily (needful) bread, and forgive us our debt as we also forgive our debtors. And bring us not into temptation, but deliver us from the evil one (or, evil); for Thine is the power and the glory for ever..

Pray this three times each day. 

Chapter 9. The Eucharist. Now concerning the Eucharist, give thanks this way. First, concerning the cup: 

We thank thee, our Father, for the holy vine of David Thy servant, which You madest known to us through Jesus Thy Servant; to Thee be the glory for ever..

And concerning the broken bread: 

We thank Thee, our Father, for the life and knowledge which You madest known to us through Jesus Thy Servant; to Thee be the glory for ever. Even as this broken bread was scattered over the hills, and was gathered together and became one, so let Thy Church be gathered together from the ends of the earth into Thy kingdom; for Thine is the glory and the power through Jesus Christ for ever..

But let no one eat or drink of your Eucharist, unless they have been baptized into the name of the Lord; for concerning this also the Lord has said, "Give not that which is holy to the dogs." 

Chapter 10. Prayer after Communion. 
But after you are filled, give thanks this way: 

We thank Thee, holy Father, for Thy holy name which You didst cause to tabernacle in our hearts, and for the knowledge and faith and immortality, which You modest known to us through Jesus Thy Servant; to Thee be the glory for ever. Thou, Master almighty, didst create all things for Thy name's sake; You gavest food and drink to men for enjoyment, that they might give thanks to Thee; but to us You didst freely give spiritual food and drink and life eternal through Thy Servant. Before all things we thank Thee that You are mighty; to Thee be the glory for ever. Remember, Lord, Thy Church, to deliver it from all evil and to make it perfect in Thy love, and gather it from the four winds, sanctified for Thy kingdom which Thou have prepared for it; for Thine is the power and the glory for ever. Let grace come, and let this world pass away. Hosanna to the God (Son) of David! If any one is holy, let him come; if any one is not so, let him repent. Maranatha. Amen.

But permit the prophets to make Thanksgiving as much as they desire.

Chapter 14. Christian Assembly on the Lord's Day. 
But every Lord's day gather yourselves together, and break bread, and give thanksgiving after having confessed your transgressions, that your sacrifice may be pure. But let no one who is at odds with his fellow come together with you, until they be reconciled, that your sacrifice may not be profaned. For this is that which was spoken by the Lord: "In every place and time offer to me a pure sacrifice; for I am a great King, says the Lord, and my name is wonderful among the nations." 

Chapter 15. Bishops and Deacons; Christian Reproof. 
Appoint, therefore, for yourselves, bishops and deacons worthy of the Lord, men meek, and not lovers of money, and truthful and proved; for they also render to you the service of prophets and teachers. Therefore do not despise them, for they are your honored ones, together with the prophets and teachers. And reprove one another, not in anger, but in peace, as you have it in the Gospel. But to anyone that acts amiss against another, let no one speak, nor let him hear anything from you until he repents. But your prayers and alms and all your deeds so do, as you have it in the Gospel of our Lord.

Full text available at Early Christian Writing site