What is the significance of the Sacraments?
There are two sacraments in the Presbyterian church, the Sacrament of the Lord’s Supper and the Sacrament of Baptism, both of which are holy signs and seals intended to be visible symbols representing Christ and all he has done for us. They are two of the means of Grace, whereby the worshipper comes close to God. This is achieved, not by the presence of the Sacrament, but rather by the faith of the worshipper and the work of the Holy Spirit.

The Lord’s Supper (I Corinthians 11.24-32) is a symbolic act by which bread and wine, symbolizing the broken body of Christ and his blood shed in sacrifice, are shared out among church members.
In the service of Communion there is a special prayer, called the Great Prayer, where the consecration of the elements take place. The elements of bread and wine remain unchanged and impart no special benefits other those brought about through their symbolic link to his sacrificial death and the very real demands that this death makes to believers' lives.

There is no right to take communion since the efficacy of a sacrament is the work of God, not of man. A general invitation is always extended  to any visitors who are members of any branch of the Christian church to share in the act of communion.
The elders bring the elements, first the bread and then the wine, from the table to the people in the body of the church. It may be customary for partakers to retain each element in their hands until all are served and then everyone partakes together.

Elders will usually not offer the elements to children but there is no reason why an accompanying parent could not ask for their child to take part. The reason is not that children are barred but that the expectation is that they don’t fully understand, or have not yet reached a point of commitment. In a church which places a great emphasis on the covenantal relationship with God there is no reason why children should not be allowed to take part if they feel that they understand the significance of the event.
Communion is celebrated in a Presbyterian Church only at periodic intervals, perhaps monthly but most commonly every three months, and is regarded as a special occasion.

Baptism (John 4.1-3) involves the use of water, usually by sprinkling or pouring it on a new member of the church, whether as an adult or child. It symbolizes the washing away of sin and being reborn into a new family in which Jesus is the head. (Galations 3.27, Romans 6.5) It is always celebrated in a service of worship as the promises made by the parents of the child or the new member are shared by all in the congregation.

Baptism is a sign of a covenant, or agreement, made between God and his people, that they all, including children, are entitled to share in his gracious gift of salvation (Mark 10.13-16). Like communion a prayer of consecration of the elements is offered but no special advantages or disadvantages come from being or not being baptized other than those that come about in the heart and mind of the believer, the greatest of which is the knowledge that the Grace of God is conferred throughout life as a work of the Holy Spirit (Acts 2.38).

The Presbyterian Church recognizes baptism in all the Christian churches and will not re-baptize.

What duties are required of elders in the celebration of the Sacrament of Baptism?
Baptism of a child assumes a Christian upbringing. There is also the expectation that with years of maturity and understanding the ‘child” will make their own personal decision to accept Christ as Saviour and Lord.

Between those events  there should many years of teaching, example and association with the local congregation.

Much of this will come from the parents whose promise regarding their children at baptism is to “teach them the truths and duties of the Christian faith and by prayer precept and example to bring them up in the nurture and admonition of the Lord and in the ways of the Church of God.”

But the other party involved is the congregation which promises “...to be faithful to your calling as members of the Church of Christ so that this child and all other children in your midst may grow up in the knowledge and love of Christ”.
It is part of the elder’s duty to see that all children of members in their district are presented for baptism. The Session also has the duty to see that a sound Christian education program is available in the church community, usually in the form of a Sunday School and Bible Class. These are no “side shows” and the Session must see that the best financial and personnel resources are available.
As part of the elder’s visitation program, he or she should remind parents, if necessary, of their baptismal vows and to see that their children attend Sunday School regularly. Here is the point where our Christian education fails – that some children attend irregularly and some not at all. 

Naturally where parents themselves attend church regularly this is so much easier.

What duties are required of elders in the celebration of the Sacrament of the Lord‘s Supper?

The elders participate in the service of Communion by sitting with the minister as he leads the service. They also distribute the elements of bread and wine to the members. There is great significance in the fact that no-one serves themselves. They serve each other. Even the minister receives the elements from another elder, usually the Session Clerk. 

Private communions are permitted under certain circumstances (e.g age, infirmity) and a minister takes at least one elder with him or her. This at least symbolizes the communal meal significance of the sacrament.

There are occasional pastoral problems associated with the celebration of the Sacrament of the Lord’s Supper.

Occasionally a parishioner feels that he or she is too unworthy to partake of communion, taking perhaps too seriously St Paul’s warning about eating the bread and wine unworthily. Elders need to make it clear to such people that the Communion is not for the righteous but for sinners only. To refuse to take communion means cutting ourselves off from the very means of grace by which we receive God’s forgiveness and help in a very special way.
Perhaps even more difficult to deal with is the attitude at the opposite extreme which says in effect “It doesn’t matter whether I attend communion or not”. What is hard to understand is how a person can ignore the words of our Lord to “do this in remembrance of me”. How can anyone refuse to join in remembering the death of our Saviour and all that it means, and so deprive themselves of communion with the Risen Lord?
Only persuasion, example and personal witness can change this attitude.

Do elders have the authority to celebrate the Sacrament of the Lord’s Supper?
In recent years, due to a shortage of ministers in the church and the unavailability of supply ministers, the General Assembly of Australia has approved arrangements whereby elders may celebrate the Sacrament of the Lord’s Supper.

This can only be done in circumstances approved by the presbytery of the bounds and in accordance with the forms of service approved by the General Assembly of Australia.