Communion, also known as the Lord's Supper, is a sacred act that should be observed by all Christians. It is a time for believers to reflect upon the price Christ paid by dying on the cross. It symbolizes Christ's body, which was given for each believer, and the blood He shed for the forgiveness of sins.
Contrary to what some may believe, communion does not have to be observed in a church. In fact, you can observe it at home whenever you wish; however, at the original event, Jesus and His disciples would have observed this time during the Passover. For the Jews, the Passover is a celebration in early spring to observe and memorialize the original Passover told in Exodus 12.
To observe the Lord's Supper, you will need these two items:
A note to make here is that communion is not meant to focus on these items, though they do have significance in what they represent. Communion is an inward expression of Christians to examine themselves and to memorialize the crucifixion of Christ and its purpose in His ministry, typified in the Passover.
Finally, you need to enter a moment of prayer to observe communion. Below is a sample prayer that you may use to observe communion on your own.
Gracious and merciful Father, who is in Heaven, I come to You in the name of Jesus. Name above all names, You are worthy to be praised. To You I lift up my eyes, to you who dwell in the heavens. I give You praise, Lord of hosts, for You are good and Your mercy endures forever.
Your word says that I must forgive the trespasses against me. Now, since You have forgiven my sins, I must forgive my brothers and sisters, not until seven times, but until seventy times seven.
I come in prayer to examine myself and to eat of this bread and drink of this cup.
Lord, I take this bread and give You thanks. Concerning this bread, You said, "Take, eat. This is My body, which is broken for you. Do this in remembrance of Me." This bread symbolizes Your body, which bore my sins as You hung on the cross, that I, being dead to sins, should live to righteousness. By Your stripes I was healed.
[Eat whatever you used to symbolize the body.]
Concerning this cup, You said, "This is My blood of the new testament, which is shed for many for the remission of sin." I thank You that You are the One who offers redemption through Your blood, the forgiveness of sins, according to the riches of Your grace. For it was You who offered Yourself as the one sacrifice for sins forever, and afterward sat down at the right hand of God.
[Drink whatever you used to symbolize the blood.]
As often as I eat this bread and drink this cup, I proclaim Christ's death until He comes. Blessed is Your glorious name forever. Let the whole earth be filled with Your glory. Amen, and amen. For Yours is the kingdom, and the power, and the glory, forever. Amen.
Extended Prayer: (From Psalm 118:21-29, which is part of the Hallel sung by Jews on Jewish holidays.)
I will praise you, for you have heard me and have become my salvation.
The stone which the builders refused has become the head stone of the corner.
This is the LORD'S doing. It is wonderful in our eyes.
This is the day which the LORD has made. We will rejoice and be glad in it.
Save now, I implore you, O LORD. O LORD, I implore you, send prosperity now.
Blessed is he who comes in the name of the LORD. We have blessed you out of the house of the LORD.
God is the LORD, who has shown us light. Bind the sacrifice with cords, even to the horns of the altar.
You are my God, and I will praise you. My God, I will exalt you.
O give thanks to the LORD, for he is good. For his mercy endures forever.
 - Matthew 26:30 and Mark 14:26 mention that Jesus and his disciples had sung a hymn before leaving for the Mount of Olives. This hymn was very likely the Hallel, which is a singing of Psalms 113-118.