What is the Gospel and How Do We Obey the Gospel?

The gospel is the death, burial, and resurrection of Jesus Christ.

"Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; by which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. 

"For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; and that he was buried, and that he rose again the third day according to the scriptures:" - 1 Corinthians 15:1-4 KJV

Apostle Peter on the day of Pentecost declared this gospel.

When asked, "What shall we do?" Peter preached how to obey the gospel.

"Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." - Acts 2:38 KJV

How do we obey Christ's death, burial, and resurrection?

Repentance is death to sin, water baptism in the name of Jesus is burial of old nature, Holy Ghost infilling is resurrection to new life.

"What shall we say then? Shall we continue in sin, that grace may abound? God forbid. How shall we, that are dead to sin, live any longer therein?  

"Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life." - Romans 6:1-4 KJV

The Holy Ghost (the Spirit) is the glory of the Father. Christ was raised up from the dead by the Spirit (the glory of the Father.)

"But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you." - Romans 8:11 KJV)

When we receive the Holy Ghost (Spirit) we not only walk in new life; we also are given the gift of eternal life.