"The fruit of the Spirit is...joy"
Whereas happiness can be fickle and ethereal, like a mood, Joy is solid-state—meaning that it operates by itself, independent of you. Happiness usually (but not always) centers around a thing, a person, an event. And this is great, but joy is different. Deeper. Again, the world has a different definition of joy than does a Christian. So the joy which I will hereafter refer to as "joy" should be understood as something coming directly from God Himself.
"The Lord God is a sun and shield..." (Psalm 84:11a)
And this is where we start. If you've never experienced a trying time or any period of suffering then it may be hard to tell happiness from joy. Joy is not contingent on anything—good or bad—that may be happening in your life. Rather, God gives His joy to those who love and worship Him. In other words, the only reason you need to have joy—true joy—is God alone. And He is always joyful—like the sun. Yes the sun in the sky, but also like the sun in space. As I'm sure you're aware, you can only get so close to the sun before you burn up. And Jesus, when he walked this earth, was ablaze with the joy of His Father, even though He knew He had to die. Jesus was always, spiritually, in the presence of His Father.
"Thou wilt shew me the path of life: in Thy presence is fulness of joy; at Thy right hand there are pleasures for evermore." (Psalm 16:11)
And here's the crux. There is actually something that we can and must do to remain in His presence and to know His joy. It's called praise and worship expressed through gratitude. Psalms says that God "inhabitest the praises" (Psalms 22:3). Again, contrasting joy with happiness, it would seem that the very circumstances that might provoke the opposite of joy should instead inspire us to thank God for who He is and that He has created and recreated us--because we never get beyond those two things: creation and recreation. And that He is always with us in said (sad?) circumstances. There is joy in His presence.
It's easy for an observer to not only want what you have, but also to mistake your joy for simple, garden-variety happiness. If they want to know, make sure you tell 'em!
In closing: "Now the God of hope fill you with all joy and peace in believing, that you may abound in hope, through the power of the Holy Ghost." (Romans 15:13)