Jesus was killed by crucifixion but, as just as he'd often said, he came back to life on the third day from his death and showed himself to his disciples and hundreds others. More about this is given on the page entitled Resurrection. But Jesus came back only to prove that he had defeated death and sin. He has now gone to be with his Father in heaven. This event was called the Ascension. This often evokes a literal image of someone flying straight up into the air as though equipped with a jet pack! But it can also be taken to mean going to a "higher place", a better place, i.e. Heaven. Following Jesus' departure the disciples worshipped God with joy and went back to the temple often (Luke 24:50-53).
Therefore Jesus is not physically here on earth anymore, but he is still very much alive and real. However, Jesus often prophesied that he would one day return (e.g. Matthew 24:30; Mark 13:24-27) to judge all people. What is he looking for? Amazingly enough he won't come with a clipboard seeing how many ticks he can put by each person's name to see if they have been "good enough" to get into Heaven, but instead he is looking for one thing - whether they have believed in him and accepted him as their saviour from sin. This is fantastic news as it means that nobody has to try to achieve something they can't - perfection; on the contrary we just have to admit that we're not perfect and need help being on God's level. Jesus is that help since he is entirely human but entirely God. In short, Jesus is the only way to be reconciled with God as he is the link between us and the Father.
So when will this happen? Don't be fooled by repeated attempts to guess or work out when Jesus will come back. For years different groups and individuals have claimed that they have had insight into when this day, Judgement Day, will come. They don't. Jesus himself warned of this and Matthew 24:36 says "But concerning the day and hour no one knows, not even the angels of heaven, nor the Son, but the Father only". Why are we not to know when this crucial event will happen? Because if we knew, people might act like nothing's going to happen until a moment before. Jesus should be central to life all the time, not just in the moment before he comes back!
When Jesus has returned, then the world as we know it will come to an end, but don't be too sad because an infinitely better new one will be created, God's Kingdom, where all who have trusted in Christ can continue living. This is Heaven, my friend!