This boils down to two questions: What are Christ's commandments? Are we still under the Law today?
The first one is interesting, because Christ boiled the law down to two main commandments: 1) Love God with your whole heart, mind and soul, 2) Love your neighbor as yourself. (Matt 22:37-39) He also gave a "new commandment": I am giving you a new commandment, that you love one another; just as I have loved you, you also love one another. (John 13:34)
There are plenty of other "commandments". Just do a Google search on "what are Christ's commandments". You'll find plenty. These aren't talked about in great detail throughout the rest of the NT, although "love your neighbor as yourself" seems the be the one with the most amount of attention.
Rom 13:9,10: For the law code, “You must not commit adultery, you must not murder, you must not steal, you must not covet,” and whatever other commandment there is, is summed up in this saying: “You must love your neighbor as yourself.” 10 Love does not work evil to one’s neighbor; therefore, love is the law’s fulfillment.
Rom 15:2: Let each of us please his neighbor for his good, to build him up.
Gal 5:13,14: You were called to freedom, brothers; only do not use this freedom as an opportunity to pursue fleshly desires, but through love slave for one another. 14 For the entire Law has been fulfilled in one commandment, namely: “You must love your neighbor as yourself.
James 2:8: If, now, you carry out the royal law according to the scripture, “You must love your neighbor as yourself,” you are doing quite well.
1 John 3:21-23: Beloved ones, if our hearts do not condemn us, we have freeness of speech toward God; 22 and whatever we ask we receive from him, because we are observing his commandments and doing what is pleasing in his eyes. 23 Indeed, this is his commandment: that we have faith in the name of his Son Jesus Christ and love one another, just as he gave us a commandment.
Now, as for the question, "are we under Law", I hesitate to get into this because it is a hotly debated topic, but here are some relevant passages.
Christ didn't come to "observe" the Law, but to fulfill it. The Greek word for "fulfill" is plerosai (Strong's 4137), which means "I fill, fulfill, complete". Christ came to fulfill, or complete the Law, not end it, but make it complete.
Luke 16:16 - The Law and the Prophets were until John. From then on, the Kingdom of God is being declared as good news, and every sort of person is pressing forward toward it.
Other passages that relate: Romans 7:3-6, all of Galatians 3; 2 Cor 3:7-14; all of Hebrews, but particularly 8:13-10:10
Hope this helps.