Orthodox baptism is generally full immersion. You would wear something white and modest that does not become see-through when wet. Some churches may have a robe for you to use, but not always.
You would also have a white outfit ready to wear after the baptism itself for the rest of the ceremony.
Many Orthodox Churches do not require a baptism for those who received a Christian baptism from another church. Instead the person goes through the second part of the Orthodox rite called Chrismation (sometimes called "confirmation"), where the person, after baptism, is anointed with holy oil, specially prepared for this purpose.
At any rate, you really should discuss this with the priest who will be accepting you into the Orthodox Church. He will be able to tell you exactly what is expected for that particular parish, some practices do vary based on circumstances.
From the Greek Orthodox Archdiocese of America website:
The Sacrament of Baptism incorporates us into the Church, the Body of Christ, and is our introduction to the life of the Holy Trinity.
Water is a natural symbol of cleansing and newness of life. Through the three-fold immersion in the waters of Baptism in the Name of the Holy Trinity, one dies to the old ways of sin and is born to a new life in Christ.
Baptism is one's public identification with Christ Death and victorious Resurrection.
Following the custom of the early Church, Orthodoxy encourages the baptism of infants. The Church believes that the Sacrament is bearing witness to the action of God who chooses a child to be an important member of His people.
From the day of their baptism, children are expected to mature in the life of the Spirit, through their family and the Church.
The Baptism of adults is practiced when there was no previous baptism in the name of the Holy Trinity.
The Sacrament of Chrismation (Confirmation) immediately follows baptism and is never delayed until a later age.
As the ministry of Christ was enlivened by the Spirit, and the preaching of the Apostles strengthened by the Spirit, so is the life of each Orthodox Christian sanctified by the Holy Spirit. Chrismation, which is often referred to as one's personal Pentecost, is the Sacrament which imparts the Spirit in a special way.
In the Sacrament of Chrismation, the priest anoints the various parts of the body of the newly-baptized with Holy Oil saying: "The seal of the gifts of the Holy Spirit." The Holy Oil, which is blessed by the bishop, is a sign of consecration and strength.
The Sacrament emphasizes the truths that not only is each person a valuable member of the Church, but also each one is blessed by the Spirit with certain gifts and talents. The anointing also reminds us that our bodies are valuable and are involved in the process of salvation.
Typical instructions for someone preparing for adult baptism can be found here;
Similar instructions from another Greek Church here;
A detailed discussion of what happens at a baptism and why can be found here: