Hi Peter
Welcome to the forum
Probably the easiest and most common way of attaching fly lines in the UK is using braided leader loops like the one below. They work, but tend to have many disadvantages, like attracting dirt and hinging etc.
I prefer to knot a length of nylon or a furled leader directly on to the fly line. I am not very good at describing how to tie knots I'm afraid, so I will cheat and link through to John Gray's excellent website ( I'm sure he won't mind )
See
http://www.trout-salmon-fishing.com/flyfishing-knots.htm#Constriction_Knot ..... The "Constriction knot" will work well on a Barrio fly line ( as do other similar nail knots ) and the "Gray's Loop" would be fine too, if you normally like to use a loop to loop connection.
I hope you find this useful
Best wishes
Mike