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According to the grace of God that was given to me
"According to the task that God freely gave me to do." (See: rc://en/ta/man/translate/figs-activepassive)
I laid a foundation
Paul equates his teaching of faith and salvation in Jesus Christ to laying a foundation for a building. (See: rc://en/ta/man/translate/figs-metaphor)
another builds on it
Another worker continues to "build" the work in the church by helping these believers spiritually. (See: rc://en/ta/man/translate/figs-metaphor)
let each man
This refers to God's workers in general. AT: "let each person who serves God."
other than the one which has been laid
After a building has been built on its foundation, the foundation cannot be changed. In this case, the spiritual foundation of the Corinthian church is Jesus Christ, built by Paul. AT: "other than the foundation that I, Paul, laid" (See: rc://en/ta/man/translate/figs-activepassive)