What is the Kingdom of God?

The Kingdom of God is anywhere God is the King.

God is King in Heaven currently.

God has assigned His son Jesus Christ to extend His Kingdom to all of existence and to rule over that existence.

1 Tim 6:13  I urge you in the sight of God who gives life to all things, and before Christ Jesus who witnessed the good confession before Pontius Pilate,
1 Tim 6:14  that you keep this commandment without spot, blameless until our Lord Jesus Christ's appearing,
1 Tim 6:15  which He will manifest in His own time, He who is the blessed and only Potentate, the King of kings and Lord of lords,

Jesus asked His disciples to pray to extend God's Kingdom to Earth so that God's will would be done there:

Matthew 6:10  Your kingdom come. Your will be done on earth as it is in heaven.

How do you join the Kingdom of God?

To be part of the Kingdom of God means that you have accepted His appointed ruler as your King and He has accepted you as His subject.

If you hear God's call to repent (give up all other gods including your self) then you can ask Christ Jesus to make you a part of His Kingdom.

If He sees that your heart is sincere and that you are genuinely offering Him control of your life, He will join you to His Kingdom:

Acts 2:21  And it will come to pass, that whoever calls on the name of the Lord will be saved.

(If you think of God as some impersonal force or object, you cannot have a real relationship with God. He is the source of love and joy, beauty and humor, intelligence and wisdom, far beyond what we have experienced! This process is not a formula you can follow - it is a matter of your heart's deepest desire and commitment and trusting Him enough to ask for His help.)

Acts 17:29  Since we are the offspring of God, we should not think that God is like gold, or silver, or stone, molded by art and man's cleverness.
Acts 17:30  And the times of this ignorance God winked at; but now He commands all men every where to repent:

Everyone in God's kingdom has been chosen by God and has also chosen to be there. Citizenship is voluntary.