Plymouth Brethren observe the Lord’s Supper on a weekly basis as a meeting on its own, usually an hour or so in length. Often this meeting is held Sunday morning before the preaching service, but it is up to each individual assembly to determine how they’ll observe the breaking of the bread.
They observe it weekly because of the pattern the describe being found in Acts 20:7, where it is mentioned in passing, “On the first day of the week, when we were gathered together to break bread…”
The saints gather together, either in a typical congregational setting of pews, or perhaps in a circle. In either case, the centrality of the room’s focus is on a table where a loaf of unbroken bread and a cup of the fruit of the vine are displayed. There is occasionally discussion over whether the bread should be an unleavened loaf and whether the contents of the cup should be fermented or not, but often these are considered secondary concerns. So long as it is bread and fruit of the vine, they are content.
The meeting usually begins in silent contemplation. Then, as men feel led by the Holy Spirit, they stand up and talk about Christ, pray giving thanks for Christ, read a passage of Scripture that reminds them of Christ, or call out a hymn that speaks of Christ to be sung acapella by the congregation. As you’ve probably picked up on, the entirety of the meeting is concerned with the person of Christ, particularly His death on the cross. This is not considered a time for preaching, exhortation, or sharing of testimonies. All things are expected to focus the believers’ hearts on the sacrifice of the Lord Jesus.
Only men are permitted to speak or pray. Women are expected to remain silent, though they are permitted to sing with the rest of the congregation. If two men stand up at once, whoever stood up first is to concede the floor to the other man. If tongues are used (taken by the brethren to strictly mean another language), an interpreter is expected or the person speaking in tongues is expected to remain silent.
When enough time has passed, one of the elders of the assembly will stand up and specifically give thanks for the bread. Then he will go to the table, tear the bread into halves or quarters, and a group of ushers or deacons will pass the bread among the assembly for the people to tear off pieces and eat. After this, another elder will give specific thanks for the cup. Then he will go to the table and either pass the single cup around the congregation, or else pass around trays of individual communion glasses. Directly after this, an offering is taken up. The offering is considered part of the worship meeting, and is typically only taken during the Lord’s Supper to encourage only believers to give and discourage unbelievers from trying to give money.
A hymn of praise is usually sung at this point, and the meeting is concluded in prayer.
In the open assemblies, since they do not have church membership and they recognize the salvation of many denominations and believe that all believers are called to remember the Lord, there are very few regulations for who is permitted to eat the bread and drink the cup (usually called “partaking of the Lord’s Supper”). Typically, the only restrictions are that a person is a Christian “in good fellowship” in a local church, meaning that they are not under church discipline anywhere. Occasionally an additional restriction of having been baptized is expected, but in my experience this is rare.
This meeting is considered the most important meeting of the church, since it was specifically requested by the Lord Himself while on earth (and apparently again after His death via the Apostle Paul in 1 Corinthians 11:23). It is often said that if you are unable to attend any other meeting in a given week, you ought to attend the breaking of bread.