Hi,
I am from Ireland (south) and got married in Venezuela nearly 8 years ago. It is very straightforward. At the time as far as I can remember I needed the copy of the Marriage course we had done, my long form birth cert and Proof of Freedom to Marry. I needed to to swear an affidavit before a Commissioner of Oaths first before bringing this letter to the Government offices. They then gave me a letter which i brought with me to Venezuela.
In Venezuela you need to have the Civil ceremony first before the Church wedding if you are planning to do so and can be done as close as days before.
Once you are married you need to have your civil marriage certificate officially translated into English, which can be done much cheaper in Venezuela. From there you can bring it to the Immigration offices (in Ireland) for them to process. I'm not sure if it is the same in the north but they usually give you residency first for the length of expiry of your (her) passport.
Hope this has been of help.
If you need any other advice please feel free to contact me.
Regards