From my Southern Baptist background, Baptism and the Lord’s Supper are two ordinances instituted by Christ for the Church.
Baptism is a symbol or sign of the work of the Holy Spirit that happens when someone is born again. It is generally one of the first acts of obedience to someone who’s heart has been changed by the work of the Holy Spirit. The purpose of baptism is to demonstrate obedience to Christ, give witness to a new life in Christ, and to celebrate someone coming to Christ. We baptize by immersion which is symbolic of the death of the old life and birth in the new life and follow the New Testament pattern of someone coming to faith and then being baptized. . Generally, the person doing the baptizing will say something like, “I baptize you my brother/sister in the name of the Father, the Son, and the Holy Spirit, we are buried with Christ in baptism and raised to walk in newness of life”. In order to be baptized you have to make a “profession of faith”. Most people who make a profession of faith have some counseling with a Pastor/Teacher before Baptism to insure that they understand what exactly faith is (Trust and Surrender that results in a changed heart and life) and what it is not (Belief alone).
The Lord Supper is an ordinance of the church that was instituted by Christ. The primary purpose of the Lord’s Supper is to remind us of the Sacrifice of Christ on the cross. The Lord’s supper is a solemn reminder of just how much Christ gave for us and how totally hopeless we are without Him. The bread and the cup are symbols of the Body and Blood of Christ and the breaking of Christ body and the shedding of His blood for our sins. By taking the Lord’s supper we remember what He did for us. In the Lord’s supper we also celebrate our faith and give thanks for forgiveness of sins and relationship with God that can only be found in Christ.
The Evangelical way of thinking is that the sacraments/ordinances help us grow in grace and knowledge of Christ and are a visible way of demonstrating our faith to others. However, they do not give us grace but help us live in and understand and mature in the grace God has given and continues to give us by our trusting in Him alone for our salvation. And that they are two of the many things in a Christian life that help us grow in Grace and Knowledge. Other things include prayer, bible study, preaching, teaching, worship, giving, serving and so forth.
Another thing you may find interesting is that while generally Baptism and the Lord’s supper are administered by Pastors/Deacons, it is perfectly fine for any Christian to baptize someone or administer the Lord’s supper. For instance, if my family is traveling or dealing with some particular crisis or are just seeking to be closer to Christ, it is perfectly acceptable for me to have the Lord’s supper with my family in my home with me serving my family.