Did Jesus tell us to follow the Ten Commandments?
As a faithful Jew He observed all 613 mitzvot (or, at least, all that would have been relevant for Him), not just the Decalogue.
And He says He came not to abolish the Law and the Prophets, but to make full.
It's in this that is crucial, "but to make full" (ἀλλὰ πληρῶσαι); I would argue we should find the proper meaning here in what St. Paul writes in Colossians,
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Therefore do not let anyone condemn you in matters of food and drink or of observing festivals, new moons, or sabbaths. These are only a shadow of what is to come, but the substance belongs to Christ." - Colossians 2:16-17
Also consider Christ's statement in Luke,
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Then he said to them, 'These are my words that I spoke to you while I was still with you—that everything written about me in the law of Moses, the prophets, and the psalms must be fulfilled.' Then he opened their minds to understand the scriptures, and he said to them, 'Thus it is written, that the Messiah is to suffer and to rise from the dead on the third day, and that repentance and forgiveness of sins is to be proclaimed in his name to all nations, beginning from Jerusalem.'" - Luke 24:44-47
Christ did not come to abolish the Law, but to make them full, to bring them to the fullness of their purpose, which is Himself and His work. The Law was never given to any people other than the Jews, as Moses says,
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Moses convened all Israel, and said to them:
Hear, O Israel, the statutes and ordinances that I am addressing to you today; you shall learn them and observe them diligently. The Lord our God made a covenant with us at Horeb. Not with our ancestors did the Lord make this covenant, but with us, who are all of us here alive today." - Deuteronomy 5:1-3
St. Paul tells us, both in Romans and Galatians, to look back to Abraham, our father in the faith; for Abraham came prior to the giving of the Law, and instead Abraham had faith "and it was accounted to him as righteousness", in this the Apostle speaks of that "righteousness apart from the law, through faith".
Because of this both Jew and Gentile are, in Christ, the children of Abraham because it is Christ who is the Seed of Abraham; the Law was given through Moses to the children of Israel and it and the covenant which God made with them at Mt. Horeb was to point beyond itself, to the Christ who was to come, that is Jesus.
Jesus did tell His fellow Jews to observe the commandments, He would not have given such a command to Gentiles however since Gentiles were outside of the covenant of the Law; a Gentile who became observant of the Law would no longer be a Gentile, but a convert to Judaism.
Thus the question of the relationship between Christians and the Torah must be understood in the context of Christ's fulfillment of those ancient covenant promises by His death and resurrection, and the giving of the Spirit on Pentecost, and the mission and constitution of the Church as the one new people, consisting of both circumcised Jew and uncircumcised Gentile, in Jesus the Messiah.
That's the long answer. The short answer would be "no", that is, no, Jesus did not tell us--Christians--to observe the Torah. And unless one is an observant Jew one has no business observing Torah as Torah isn't meant for you if you're an uncircumcised goy.
What Christ does command, however, is the Great Commandment, "Love the Lord your God with all your heart, with all your soul, and with all your might; and love your neighbor as yourself" This is the heart of God's Law. And the royal law of love
is commanded of Christians, both Jew and Gentile.
-CryptoLutheran
