Definition for the word baptism is "a rite of washing with water as a sign of religious purification and consecration.”
In Mt 28:19, the Lord Jesus commands his disciples to preach the gospel and baptize those who believe it in the name of the Father, the Son and the Holy Ghost. Baptism is actually just the Greek word for "immerse". Thus, Christ wants believers to be immersed in water.
The prerequisite for baptism:
"And as they went on [their] way, they came unto a certain water: and the eunuch said, See, [here is] water; what doth hinder me to be baptized? And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God." - Ac 8:36,37
The purpose of baptism:
By being immersed, a believer identifies with the death, burial and resurrection of the Lord Jesus Christ. He/she also testifies in public that he/she has become a disciple of the Lord Jesus Christ.
Common misconceptions about baptism (and the corresponding truths):
Baptism can be done by sprinkling, or pouring water on the person. Solution to misconception: drop the Greek and start using English instead.
Baptism is necessary for salvation. Eph 2:8,9 says we're saved by grace (God's unmerited favor), not by works, lest anyone should boast. If baptism was necessary for salvation, people doing baptism could take credit for sending others to heaven - that would be abominable to God.
Baptism is sufficient for salvation. You can't get to heaven unless your sins are forgiven. Nowhere in the Bible are we told that baptism takes away people's sins. We are told that forgiveness of sins is available through Jesus Christ (Ac 13:38), based on the shedding of his blood (Col 1:14). Mk 16:16 makes it clear that belief + baptism is sufficient for salvation, belief being the necessary ingredient.
We get the Holy Spirit upon baptism. Ac 10:44-48 clarifies that this is not the case. The Holy Spirit descended upon Jesus like a dove when he was baptized. It is wrong to draw a parallel between us and Jesus because his baptism was an inauguration of his ministry, not a symbol of his having turned from sin like us!
The Lord's Supper
Whereas baptism is an identification with the death of the Lord Jesus, the Lord's Supper is a proclamation of the same thing.
Titles used in scripture for this ordinance:
The Lord's supper (1 Cor 11:20) - This title connects this act with the passover supper where the Lord Jesus instituted it, recorded in the synoptic gospels. Each family would have the meal together, with the head presiding, around the unleavened bread, wine, the roasted lamb, the bitter herbs, etc. The presiding person would take the first cup called the cup of blessing, bless it and pass it on. Then they will have the bitter herbs with fruit sauce, reminding them of Egypt. The head of the family would give a sermon explaining the meaning. They'd sing Ps 113, Ps 114, and pass on a cup of wrath, not drunk, but poured out, representing the plague on the Egyptians, then they'd eat the unleavened bread with prayer, then there was a cup called the cup of salvation then Ps 115-118, the wine again, called the cup of the kingdom that's coming. At the time of the third or fourth cup, the Lord Jesus instituted the Lord's Supper. He took the unleavened bread and gave it. He gave the wine as well, saying this is the wine. He asked them to keep this until he comes. The meal reminds them of the Egyptian deliverance; for us our deliverance from sin and Satan. The Lamb was slain.
Breaking of bread (Acts 2:42): In Israel, after a death of a person , after the burial, people would visit the home, and break bread there, Jeremiah 16:7. This was an act of consolation and fellowship. For us, we're remembering the one who died and celebrating the resulting fellowship that we have with each other.
Note: that the Lord's Supper is not an occasion when God imparts saving grace to us. When we received Jesus Christ as our personal Lord and Savior, we were completely justified - we don't need anything more to be done in that direction.
The importance of the Lord's Supper: 1 Cor 11:23-30. This centers around various features.
The Source: Paul has received it from the Lord Jesus. The word received (paralambano) is used for things received from one's father, to be passed on to others, something to be revered. In the 10 verses from 23 to 32, Lord is mentioned 7 times, emphasizing the authority of Jesus over this ordinance, and over us.
Time of institution: "On the night when he was betrayed". Judas Iscariot walked out just before it was instituted. Thus it was instituted when the world was out to betray him. Thus it was an ordinance of love.
The duration of its performance: "This do ye, till he come". The Jerusalem church evidently kept the Lord's supper everyday. Towards the end of the apostolic age, it was kept on the first day of the week (Acts 20:7). Some things in the apostolic age were temporary, not this, indicating its importance.
The meaning: The Lord's Supper is also important because of its great meaning.
What is the meaning of the Lord's Supper?
It shows the death of the Lord Jesus (Luke 19:24,25, 1 Co 11:26). The cup is the cup of the new covenant. In the OT there were 2 important sprinklings of blood. In Leviticus 8, Aaron and his sons were consecrated for service. In Leviticus 14, a leper was cleansed. Thus it indicates separation for service and cleansing. Both these meanings were intended for the Israelites when Moses sprinkled blood on the people in Ex 24:8. In Jeremiah 31, God says He'll make a new covenant, which means a new testament, also with blood. For the old, it was animal blood, here Jesus' blood, which speaks of the life he laid down. Cleansing and separation are implied here. This meaning is in the PAST.
The Lord's Supper also conveys the meaning of the communion that we have as one body (1 Cor 10:16,17). That is why we keep only one loaf. This meaning is in the PRESENT.
It anticipates the coming of Jesus. This meaning is in the FUTURE.
The Participants in the Lord's Supper:
The participants should be the members of Church of God. These are those who have been saved (Ac 2:47), by faith.
The participants should be baptized: In Mt 28:19, 20, observance of commands like the Lord's supper, comes after baptism. In Ac 2:41,42 the same order is maintained. We can't choose one ordinance over the other. Doctrinally speaking, all believers have a part in the Lord's supper. Practically, in keeping with apostolic practice, those who take the Lord's supper have to have regard for baptism.
The participants should be in good state: "Let a man examine himself." (1 Cor 11:27-30)