The Sacrament

The important word Luke used in describing the sacrament that Nephi also used but Paul did not.
The important word that Luke used in describing the sacrament was REMEMBER. It is so often that people forget why we take the sacrament or what the ideal purpose of taking the sacrament is all about. 
In Luke 22:19 it says, "And he took bread, and gave thanks, and brake it, and gave unto them, saying, This is my body which is given for you: this do in remembrance of me." Christ told us that we need to take the sacrament in remembrance of him. Also stating in Moroni 4:3 Moroni says, "O God, the Eternal Father, we ask thee in the name of thy Son, Jesus Christ, to bless and sanctify this bread to the souls of all those who partake of it; that they may eat in REMEMBRANCE of the body of thy Son, and witness unto thee, O God the, the Eternal Father, that they are willing ti take upon them the name of thy Son, and ALWAYS REMEMBER him, and keep his commandments which he hath given them, that they may always have his Spirit to be with them. Amen." As we partake the sacrament we need to really remember what Christ has done for us. I know that before partaking the sacrament I think of all the things that I've done that week and ponder to see if I am worthy enough to take the sacrament. Then as they say the sacrament prayer in sacrament meeting I listen to the words that are said and remember what Christ has gone through for me and for my fellow beings. He died for our sins! 
What is the difference between what is taught in 1 Corinthians 11:27-29 and 3 Nephi 18: 28-29 with regards to the counsel about when to not partake of the sacrament?
In 1 Corinthians 11:27-29 it says, "27. Wherefore whosoever shall eat this bread, and drink this cup of the Lord, unworthily, shall be guilty of the body and blood of the Lord. 28. But let a man examine himself, and so let him eat of that bread, and drink of that cup. 29. For, he that eateth and drinketh damnation to himself, not discerning the Lord's body." In 3 Nephi 18: 28-29 is also says, "...whoso eateth and drinketh my flesh and blood unworthily eatheth and drinketh damnation to his soul." We should not partake the sacrament unworthily because it's like we are mocking Jesus Christ. The only way to cleanse imperfection and impurity is obedience. As we obey the commandments and are true to our beliefs we can have faith which leads to repentance, which leads to baptism (sacrament and temple), and which also leads to having the gift of the Holy Ghost. When we continue to keep the commandments and are honest to ourselves and the Lord when taking the sacrament, those things will increase and make us stronger in the gospel. 
What did Paul teach that explains why we don't want to partake of the sacrament unworthily?
We don't want to partake the sacrament unworthily because we will be damned. We are to take the sacrament to remember all the things that the Lord has done for us, not mock him.
What can you do to make the sacrament a more meaningful experience in your life both on Sundays and during the week?
I think what I can do is to be true to myself. Know when it is right for me to take and not take the sacrament. I know that in order to always have the spirit to be with me, I would need to be honest in all my doings. Even when it's hard sometimes to not take the sacrament because people will know, it's better for you to let people judge rather than play God.