This is an excellent article by Jesse Johnson that was posted at The Cripplegate.
How does a person know if they have been predestined by God for heaven? The shortest answer to the question is also the best: Do you love Jesus? If so, then you have been predestined.
Unpacking that short answer shows you the Trinitarian nature of salvation. The Father predestined us before time (Ephesians 1:4). This predestination is expressed through adoption into his family through faith in his Son, Jesus (Ephesians 1:5). This faith is expressed by confessing Jesus as Lord (Romans 10:10), and nobody can do that unless the Holy Spirit is indwelling them (1 Corinthians 12:3).
When the Holy Spirit saves a person, He gives them a new nature—He gives them a heart of faith to replace their heart of stone (Ezekiel 36:26). The person goes from living for himself to living for Christ. The person goes from hating God to loving God through Jesus.
Thus an individual knows they have been predestined for salvation only when they believe the gospel, and see in their heart faith and love for Jesus Christ.
Taken together, our Triune God predestines, then sends his Son who accomplishes salvation, then sends his Spirit who applies salvation. All three persons of the Trinity are at work in our salvation. They have the same will, the same love, and the same intent. Thus the doctrine of predestination breaks into this world through every heart that loves Jesus.
A person obviously doesn’t need to know all that in order to be saved. Instead, what a person needs to know in order to be saved is that they are a sinner, and are unable to save themselves by their own good work. Yet Jesus, who is the Son of God, died on the cross for our sins, and rose triumphantly from the grave having atoned for sin. Because of depravity, nobody would savingly believe that unless the Holy Spirit was enabling them.
To approach this from yet another direction: a person can only know if they have been predestined when they are saved, and salvation is evident in a love for Christ. That love is imperfect, and waxes and wanes through life, of course. But the only window we have into the saving and predestining power of God in the heart of each person who trusts Christ. There is no way to trust Christ for salvation without the regenerative work of the Holy Spirit, He only saves those whom the Father has chosen, and all whom He saves will express that through a love for Jesus.
How do you know you have been predestined? The only way is by placing your faith in Christ.
Fortunately the opposite answer is not true—a person cannot say they have not been predestined simply because they don’t believe in Jesus now. Who is to say they won’t believe in the future? So if you are concerned you have not been predestined, ask yourself this: Do you want to believe the gospel? Do you wish you were going to heaven?
Then there is no magic to it, and no fatalism needs be involved. All who call upon the Lord can be saved. And once saved, they will see they were called by Him all along.