Let us let the LBC speak for itself.
http://www.spurgeon.org/catechis.php
1. Q. What is Baptism?
A. Baptism is an ordinance of the New Testament, instituted by Jesus Christ (Matt. 28:19), to be to the person baptised a sign of his fellowship with him, in his death, and burial, and resurrection (Rom. 6:3; Col. 2:12), of his being ingrafted into him (Gal. 3:27), of remission of sins (Mk. 1:4; Acts 22:16), and of his giving up himself to God through Jesus Christ, to live and walk in newness of life (Rom. 6:4-5).
________________________________________
2. Q. To whom is Baptism to be administered?
A. Baptism is to be administered to all those who actually profess repentance towards God (Acts 2:38; Matt. 3:6; Mk. 16:16; Acts 8:12, 36-37; Acts 10:47-48), and faith in our Lord Jesus Christ, and to none other.
3. Q. Are the infants of such as are professing to be baptised?
A. The infants of such as are professing believers are not to be baptised, because there is neither command nor example in the Holy Scriptures for their baptism (Exod. 23:13; Prov. 30:6).

4. Q. How is baptism rightly administered?
A. Baptism is rightly administered by immersion, or dipping the whole body of the person in water (Matt. 3:16; Jn. 3:23), in the name of the Father, and of the Son, and of the Holy Spirit, according to Christ's institution, and the practice of the apostles (Matt. 28:19-20), and not by sprinkling or pouring of water, or dipping some part of the body, after the tradition of men (Jn. 4:1-2; Acts 8:38-39).

I believe it is very important to emphasize the difference between two different groups that believe in ‘Believers Baptism’.
Dispensationalist, Mennonites do not appreciate God’s fundamental unity of the Bible and God’s covenant dealings with His people. Therefore they reject paedobaptist arguments from the covenants and regard the New Testament data as by itself conclusive for believer’s baptism. In other words they say that was just Old Testament teaching, this is the New Testament.
That group gets the scorn of the Reformed paedobaptist community and rightfully so.

Reformed Baptists on the other hand like their Reformed paedobaptist brothers and sisters recognize that the Old Testament is still relevant. However, believe that it supports their positions, not the Reformed paedobaptist position. There is a certain parallel between Old Testament circumcision and baptism (Romans 4:11; Col. 2:11-12). Both were rites or symbols induction into the covenant people of God. For more, I recommend ‘A Modern Exposition 1689 Baptist Confession of Faith.