Rightly dividing the word of truth is simply recognizing the divisions that God has placed in the Bible. "Study to shew thyself approved unto God, a workman that needeth not to be ashamed, rightly dividing the work of truth.  2 Timothy 2:15.  These divisions are commonly called dispensations or ages.

Put succinctly, a dispensation is a God-revealed body of information given for man's obedience during a certain period of time.

We live during the dispensation of grace.  Ephesians 3:1-4, "For this cause I, Paul, the prisoner of Jesus Christ for you Gentiles, If ye have heard of the dispensation of the grace of God which is given me to you-ward: How that by revelation he made known unto me the mystery; (as I wrote afore in few words, Whereby, when ye read, ye may understand my knowledge in the mystery of Christ.)

The dispensation of grace began in the mid-Acts period (i.e. Acts 9-15.) Since the dispensation of grace was given to the Apostle Paul, the dispensation of grace could not have begun before Paul was saved in Acts 9. In Acts 15, the Jerusalem Council is convened to discuss the different gospel that Paul had been proclaiming, so it is apparent that Paul must have received his mystery information before Acts 15.

You should not take anyone else's word for anything.  The Bible is the authority.  No man is your judge.  Therefore, you need to be fully persuaded in your own mind.  Acts 17:11, "These were more noble than those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so."