The first place to go is to the rector of the church you would like to get married in – you do not necessarily need to be a member of a congregation to be married in an Episcopal Church in Edinburgh. The rector will outline the process for that particular church. This is likely to involve meeting with the rector for a number of sessions of marriage preparation, some churches also run a more detailed marriage preparation course where you will be able to join with others who are also preparing for marriage.
The rector will talk with you about the practicatlities and about church teaching around marriage. He or she will need to seek the permission of the bishop if either of you have been married before, or if you wish to have a Christian service in a building other than the church. The rector will be able to advise you on this.
The rules for getting married in Scotland are governed by the Register General for Scotland, and you must go through the process of applying for a ‘schedule’ from them. There are strict timescales for this process. A marriage cannot take place without this document. The City of Edinburgh Council has an informative Birth, marriage/civil partnerships and death section which can also advise.