Jesus Christ instituted the Lord's Supper the night before He was crucified (Matt. 26:26-29; Mark 14:22-26, Luke 22:15-20, 39).
Matthew 26:26 "And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, Take, eat; this is my body. 27 And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it; 28 For this is my blood of the new testament, which is shed for many for the remission of sins. 29 But I say unto you, I will not drink henceforth of this fruit of the vine, until that day when I drink it new with you in my Father's kingdom."
The Lord's Supper is done in "remembrance" of Him.
Luke 22:19 "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. 20 Likewise also the cup after supper, saying, This cup is the new testament in my blood, which is shed for you."
Roman Catholics call this "Mass" and believe that the bread is literally His body and the new wine (grape juice/Matt. 26:29) is literally His blood. Jesus Christ died once and does not need to be continually sacrificed (Heb. 10:10). Besides that, drinking blood is forbidden before the law (Gen. 9:4), under the law (Lev. 17:12) and even under grace (Acts 15:29).
In 1 Corinthians 11, Paul gives us more light on the Lord's Supper. He makes it clear that the Lord's Supper is an ordinance to be observed by saved Christians.
1 Corinthians 11:2 "Now I praise you, brethren, that ye remember me in all things, and keep the ordinances, as I delivered them to you."
1 Corinthians 11:23 "For I have received of the Lord that which also I delivered unto you, That the Lord Jesus the same night in which he was betrayed took bread:"
As said before earlier, the Lord's Supper is done in remembrance of Christ's shed blood and broken body. His body was broken because of the spear that the soldier put in his side on the cross. His bones were not broken though.
John 19:36 "For these things were done, that the scripture should be fulfilled, A bone of him shall not be broken."
Not only are we to remember His First Coming, but also His Second Coming when He comes to reign as King for 1k years. Also, notice that in verse 26 it says, "as often as". This means that there is no set rule on how often to partake in the Lord's Supper. That decision is usually left up to the Pastor, who looks after the spiritual condition of his local church.
1 Corinthians 11:26 "For as often as ye eat this bread, and drink this cup, ye do shew the Lord's death till he come."
Another vital thing to do before partaking of the Lord's Supper is to examine ourselves and make sure we do not have any unconfessed sins in our life. Those that do not examine themselves before partaking receive "damnation", which is not Hell, but the person getting "weak", "sickly" or even dying (sleep). Verse 34 explains that the reason for the Lord's Supper is not to satisfy the belly.
1 Corinthians 11:28 "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 unworthily, eateth and drinketh damnation to himself, not discerning the Lord's body. 30 For this cause many are weak and sickly among you, and many sleep."
1 Corinthians 11:34 "And if any man hunger, let him eat at home; that ye come not together unto condemnation. And the rest will I set in order when I come."
Those are the rules and instructions for the Lord's Supper. Any other rules that any other church adds to it is not scriptural. This includes "Closed Communion", which limits only the members of that local church to partake in the Lord's Supper. No where does Paul or Jesus give those requirements. Scriptures are clear that it is the responsibility of the believer to examine his own self by self-judgment and prayer.
The Pastor's job is to make sure everyone knows the rules and requirements before eating and drinking. The Lord's Supper is for the Body of Christ. "Closed Communion" is very popular with Baptist Briders, who believe only those in their local Baptist church are the Bride of Christ, which is false doctrine. Everyone that is saved by faith alone today until the Rapture is the Bride of Christ (Body, Church).
For example, Paul traveled from church to church. Would you deny that Paul partake in the Lord's Supper just because he's not in your church membership? Paul includes himself in the same body of the Romans, Corinthians and Ephesians (Rom. 12:5, 1 Cor. 10:17, Eph. 5:30).
"Open Communion" means that the Lord's Supper (Communion) is open to all saved believers that have examined themselves. With that said, Christians should not avoid joining a local church. Every saved believer should find a King James Bible Believing Baptist church for preaching, teaching, hymns, fellowship and etc. We are commanded in scripture not to forsake the assembling together of ourselves at a local level. The Lord's Supper should bring a church closer together (1 Cor. 17-18).
Hebrews 10:25 "Not forsaking the assembling of ourselves together, as the manner of some is; but exhorting one another: and so much the more, as ye see the day approaching."