Will we be judged as far as our eternal destiny if we don't observe the Sabbath?
In Romans 1:5, we have received grace in order to bring about the obedience that faith requires, so we are not saved by our obedience, but rather the same grace and faith by which we are saved also requires our obedience. It's not my call whether breaking the Sabbath will bar someone from heaven, but rebellion against God is never a good thing.
What day do we or are supposed to celebrate the Sabbath?
The Sabbath is the 7th day, commonly referred to as Saturday, though it technically begins on Friday at sundown.
How do we go on celebrating the Sabbath since it is in the Ten Commandments?
Keeping the Sabbath is really easy and we must resist attempts to make it complicated. There are 24 chapters worth of instructions in the Mishnah for just how to keep the Sabbath, which rigorously define what it means to work everywhere from how much someone can lift to how far someone can walk before it counts as work, whereupon they then put a fence around that to scale it back in order to prevent anyone from accidentally doing something that could count as work. While it is certainly important to understand how to correctly keep the Sabbath and they certainly had good intentions, there is a danger in that they then ended up taking what was supposed to be a day rest focused on God's love for us and perverting it into a legalistic chore focused on the minutia. If someone were to spend the Sabbath worried about whether they were resting correctly, then they would be missing the whole point and would not be resting correctly.
So keeping the Sabbath is simple and we all have a basic understanding of what is work and what is not. The point of refraining from work is so that we can make time dedicate to delighting in God's love for us as a community of believers. Part of that delight comes from the preparation of getting tasks done ahead of time on the day before so that they don't serve as interruptions.
Has it been done away with since we are in the New Testament?
None of God's eternal laws have been and will ever be done away with. In 1 Peter 1:13-16, we are told to have a holy conduct for God is holy, which is a quote from Leviticus where God was giving instructions for how to have a holy conduct, which straightforwardly includes keeping God's Sabbaths holy (Leviticus 19:2-3). Eternal instructions for how to act in accordance with God's holiness can't be done away with without first doing away with God's eternal holiness.
Jesus said that He is the Fulfillment of the Law,
"To fulfill the Law" means "to cause God's will (as made known in the Law) to be obeyed as it should be" (NAS Greek Lexicon pleroo 2c3). After Jesus said he came to fulfill the Law in Matthew 5, this is precisely what he then proceeded to do six times throughout the rest of the chapter by teaching how to correctly understand and obey it. In Galatians 5:14, loving your neighbor fulfills the entire law, so it refers to obeying the Law as it should be obeyed, and refers to something countless people have done, not to something unique to Christ. Likewise, Galatians 6:2 says that bearing one another's burdens fulfills the Law of Christ, so you should interpret it in the same way as fulfilling the Law and the Prophets, namely obeying it as it should be, not as doing away with it. In Romans 15:18-19, it says that Paul fulfilled the Gospel, which again referred to causing Gentiles to become fully obedient to it in word and in deed, not to doing away with it.
so what did He mean that we are supposed to follow the Sabbath as Christians?
A Christian is by definition someone who follows Christ, so when Christ set an example for us to follow of how to keep the Sabbath, then we should follow his example.