There is actually an order of service. When we gave our notice of intention to marry last year, we got a print out of the wording of the service, which includes the order in which it happens and optional things you can include. You can then add your own bits and pieces such as music, readings, poetry, lighting of unity candle etc, so long as none of it is religious in any form.
As I remember it, we did it sort of church like, husband to be was there before me, I arrived, Dad walked me up the aisle (little), registrar introduced herself, introduced us, said why we were here, that we had already declared intention to marry and gave date, asked again if there either of us were there under duress, any reason why we should not marry etc etc etc. Pronounced us man and wife, kisses, hugs, claps, sign the paperwork and off with you. We had music, a poem, single candle lighting by each Mammy to signify the two families (and make them feel involved) and lighting of unity candle by us and it still only took 20 minutes. Would highly recommend it. Quick, efficient and as personal as you want to make it. Registrars are very accommodating.