With the assumption that when you mention "people in the time of Jesus" you are referring to the first people who were directly influenced and taught by Jesus and his apostles, the best description of the first Christian groups in existence is found in the New Testament of the Bible in the book of the Acts of the Apostles. This account was written by Luke, who also wrote the Gospel of Luke. He wrote the Acts partially from the accounts of eyewitnesses and partially from firsthand experience. Besides believing in the words of Jesus, these early followers had a much more radical concept of Christian life than we do today. They lived a lifestyle in which all of their personal possessions were at the disposal of the larger Christian group. As Luke writes in Acts Chapter 4 verse 32:
And the multitude of them that believed were of one heart and of one soul: neither said any of them that aught of the things which he possessed was his own; but they had all things common.
In other words, no one suffered deprivation because everyone shared all that they had. This system seemed to work well for them, as Luke explains in verses 34 and 35 of the same chapter.
Neither was there any among them that lacked: for as many as were possessors of land or houses sold them, and brought the prices of the things that were sold, and laid them down at the apostles's feet: and distribution was made unto every man according as he had need.
We assume that the people who sold houses were selling extra ones. Later in the story Luke clarifies that Christians still had houses to live in, and that sometimes they lived communally. It is also clear from the text that this selling of possessions and giving to the group was voluntary. However, in the fervor of their love for Jesus and each other, they chose to do these actions for the good of all.
Later, the apostle Paul, after his conversion, made the first missionary journeys and established Christian enclaves in the areas now known as Turkey and Greece. Various Christian groups kept in touch by messenger and helped each other out in time of need. When the church in Jerusalem received persecution and went through a famine, churches in outlying areas sent aid in the form of financial gifts.
Over time, as the Christian church became larger and more institutionalized and even split up into various denominations and factions, the close bond by which Christians would gladly give up all their possessions for each other was lost. Christians still believe in the teachings of Jesus as put forth in the Bible, but they generally live in isolated family units and primarily see to their own needs. The Christian belief in helping others with charitable giving remains the same, but nowadays most Christians offer only a small percentage of their possessions to others. This is opposed to the intense fervor adherents felt in the time of Jesus and directly after that inspired them to share everything.