BOOK: The Person and Ministry of the Holy Spirit
Chapter 1.2: Working of the Trinity

1.2    Working of the Trinity

There is a specific order1 of authority and work in the Trinity.  The Father is the greatest2, Jesus sat down in His throne and was given dominion, and the Holy Spirit is performing the transformation work with you.  While each member of the Trinity is equal with each other3, God is not the author of confusion.  Without a level of authority and system of work responsibilities, there is always confusion.
I Cor     12:4-6
Now there are diversities of gifts, but the same Spirit. 
And there are differences of administrations, but the same Lord. 
And there are diversities of operations, but it is the same God which worketh all in all.
The Trinity works much like a cooperation:
The Father (God-v6) is the Chief Executive Officer, who decides what the company's line of business is, and generally how it is going to accomplish it.

Jesus (Lord-v5) works as the administrator or mediator and head over all things. His job is to see that the actual goals are accomplished. 

The Holy Spirit acts as a first line supervisor, or your immediate boss.  He recruits for the company, trains you, equips you with the necessary tools (gifts), and supervises and directs your activities.
You will notice that the Motivational gifts in Romans 12:3-8 are given by God - the Father to motivate you to work in the company to help accomplish the overall plan.

The Five Fold Ministry gifts in Eph 4:8-16 are given by Jesus.  The five fold perform the administration work of equipping and training the Body to go forth with the gospel.

The Charismatic gifts in 1 Cor 12:7-11 are given by the Holy Spirit to equip the believer with the necessary tools to do the actual work.

1. Matt 28:19, 1 Cor 13:13
2. John 8:42, 14:28
3. Phil 2:5