As signs, they are visible words that show us the truth of the Gospel.
As God's actions they make our relationship with Him official.
As God's presence they put us in communion with God, though only by faith.
Baptism brings us into the visible church.
It is an act of repentance (normative perspective - Acts 2:38), cleansing (situational - Acts 22:16), and union (existential - Rom 6:1-4).
It confirms our membership in the covenant with God. So it isn't just a symbol (a la Zwingli), and it isn't the new birth itself (a la Rome).
Mode of baptism
Some say baptism must be by immersion. Baptize means immerse. John the Baptist baptized where there was "much water" (John 3:23). Jesus came up out of the water at His own baptism (Matt. 3:16). Our death and resurrection with Christ is better symbolized this way (Romans 6:2-6).
Others say baptism isn't always by immersion. Luke 11:38 uses "baptize" for a ritual washing. "Much water" in John 3:23 wasn't necessarily for immersing. "Some locations of baptism make immersion unlikely (Acts 9:11, 18; 10:25, 47; 16:32-33)" (1064). There are no examples of baptism in the NT that must be by immersion. Many Scriptures use the word baptism but the meaning is a sprinkling (Hebrews 9:10; 10:22; 12:24; 1 Peter 1:2), or the Spirit is said to be poured on us (Acts 2:17, 33; Rom 5:5).
Credo-baptists (CB) believe one should not be baptized until he can profess faith on his own.
Paedo-baptists (PB) believe infants (Greek = paedo) should be baptized.
CB says there is no NT command to baptize infants. THe NT always links baptism to a profession of faith of an adult. The NT is radically different from the OT such that we apply sacraments to individuals with faith, not to all those in a household.
PB says the OT commanded the circumcision of infants, and baptism is doing now what circumcision did then. God's covenant remains for the children, too (Acts 2:39). Jesus blessed children, a covenantal act (not a sentimental one!). NT baptisms are mostly household, rejecting the idea that the NT is newly individualistic, even if infants weren't part of those households.
The Lord's Supper
The Supper has past, present and future meaning. We remember Christ's death in the past, commune with Him in the present, and look forward to the Marriage Supper of the Lamb in the Consummation.
Presence of Christ
Rome says the bread and wine are physically turned into Jesus' body and blood.
Lutherans say the bread and wine are somehow physically conveying Jesus' body and blood.
Both of these don't get the representation meant by the bread and wine.
Most Protestants follow Zwingli who said the bread and wine are just symbols.
Calvin said Christ is really present, but not physically in the bread and wine.
The point of the meal is to express restored reconciliation with God. Tabernacle and temple both had bread and wine on tables within. Wisdom invites us to her feast (Prov. 9), and Jesus multiplied bread for the multitudes.