There are as many expressions of baptism and communion (a.k.a. The Lord’s Supper) as there are churches. The question that we must ask is, “What does the Bible say about these ordinances?” I will go ahead and tip my hand–I am a Southern Baptist. Thus, my explanation and Scriptural support will point to Baptist beliefs. However, the Bible is the ultimate authority on how these ordinances are to be practiced. As such, we must submit our beliefs to the authority of Scripture. Both baptism and communion are expressions of our faith in Jesus.
There are three methods of water baptism that are used in Christian churches today: immersion (in which the person is completely submerged), affusion (which is, pouring), and aspersion (sprinkling).
Christian baptism, in accordance with the New Testament, is by immersion only.
And when Jesus was baptized, immediately he went up from the water…
The word baptizo in Greek, translated “baptize” in the New Testaments, meant to “dip” or “immerse.”
Whenever the act of baptism is described in the New Testament, the one who is baptized actually goes into the water. Thus, after Jesus was baptized, He “came up out of the water” (Matthew 3:16, Mark 1:10), and when Philip baptized the Ethiopian eunuch, “they both went down into the water” (Acts 8:38). 
Baptism does not provide a person salvation. It is done as a symbolic expression of what has already taken place in their life. The symbol it represents is the death, burial, and ressurection of Jesus. The person who is baptized is saying that they have died to their old life and are raised to walk a new life in Christ.
While not necessary for salvation, baptism is an important act of obedience. Baptism is the first public action that shows one’s identification with Christ. It is a witness to all about the faith of the one being baptized. Thus, only people who have given their lives to Christ may be baptized.
Communion (a.k.a. The Lord’s Supper)
The Lord’s Supper is a symbolic act of obedience whereby members of the church, through partaking of the bread and the fruit of the vine, memorialize the death of the Redeemer and anticipate His second coming. 
Jesus established this as a commemoration of His death (Matt. 26:17-30; Mk. 14:12-26; Lk. 22:7-23). The focus of the supper is remembrance and thanksgiving.
Just as with baptism, the supper provides no saving power. Those who eat the bread and drink from the cup who are unsaved remain unsaved. Again, this is a symbolic memorial feast.
For I received from the Lord what I also passed on to you: that the Lord Jesus, on the night He was betrayed, took bread, and when He had given thanks, He broke it and said, “This is My body, which is for you; do this in remembrance of Me.” In the same way, after supper He took the cup, saying, “This cup is the new covenant in My blood; do this, as often as you drink it, in remembrance of Me.” For as often as you eat this bread and drink this cup, you proclaim the Lord’s death until He comes.
1 Corinthians 11:23-26
Paul emphasized that we are taking the elements in rememberance of Christ and what He did on the cross. Each time we take the elements we are proclaiming Jesus’ death. The supper is to remind us and others of the sacrifice that Chirst made on our behalf.
 “Is Baptism by Immersion the Only Correct Way to be Baptized?,” accessed at http://www.equip.org/article/is-baptism-by-immersion-the-only-correct-way-to-be-baptized/
 “The Baptist Faith and Message,” accessed at http://www.sbc.net/bfm2000/bfm2000.asp