The early Church worshiped God wherever it could: in houses, outside, in catacombs underground. While the worship — the liturgy — of the Church has developed over time, how we worship God today in the Orthodox Church would feel similar to how Our Lord Jesus Christ celebrated liturgy Himself in the Jewish temple.
“And the people waited for Zacharias, and marveled that he lingered so long in the temple. But when he came out, he could not speak to them; and they perceived that he had seen a vision in the temple, for he beckoned to them and remained speechless. So it was, as soon as the days of his service [liturgy, in Greek] were completed, that he departed to his own house.”
Luke 1:21-23
Our worship is focused on God, but it is deeply corporate, since all the Church together — the Body of Christ, the saints living and departed, along with the angels — celebrates the Divine Liturgy. It is an experience of body, spirit, and soul, and, there, we join with the eternal Divine Liturgy, as opposed to creating it. In other words, we participate in something much larger than us.
“Again, the next day, John stood with two of his disciples. And looking at Jesus as He walked, he said, ‘Behold the Lamb of God!’ The two disciples heard him speak, and they followed Jesus. Then Jesus turned, and seeing them following, said to them, ‘What do you seek?’ They said to Him, ‘Rabbi’ (which is to say, when translated, Teacher), ‘where are You staying?’ He said to them, ‘Come and see.'”
John 1:35-39
When you visit an Orthodox Church for the first time, come to see. More about the worship of the Church can be found here. For a practical guide on visiting, including etiquette, please see this site.