On Monday we remember the angels, who were the first to be created by God. Most people don't actually do anything, but monks fast on Mondays.
On Wednesday we remember Judas' betrayal of Jesus and therefore we fast.
On Friday we remember the crucifixion of Jesus and therefore we fast.
On Saturday we remember the whole of the first creation, not by following the Sabbath of the Law but by praying for the dead who have entered rest and by getting prepared for communion on the next day. We specifically do not fast.
On Sunday, we remember the new creation, the resurrection of Jesus, Easter. Eucharistic liturgy is necessary on that day.
What should you do on the Sabbath? Remember what Jesus did on the Sabbath: His lying in the tomb, His rescue of those who were held in Hell, and the repose of those who have died since then. You don't need to read the Bible all day long, but you should at least prepare yourself mentally and spiritually for the eucharistic liturgy that will happen the next day, and so not dedicate too much time to secular endeavors. Maybe dedicate a part of the day to reading a Church Father, and definitely take some time to pray for the dead.
t. Orthodox so I have no clue if Catholics and Protestants do the same thing or if this even applies to you, but I hope it's not a bad suggestion at least.