You are definitely trusted with the role of godfather by your friend on his or her child if you are attending a baptism for your god child you are not just attending for the role of moral support you are attending the godfather you now have a duty in the life of the child just as the parents have a role in the life of the child, i don't know how it is done in other countries but in my country as a godfather if you are attending the baptism of a child whose parents name did the godfather first of all you are expected to provide a maiden name for the child which you may actually call the child of your own accord.
Now secondly you will have to be there to advise the parents on how to raise the child , although since you're only a godfather you are only raising a suggestion depends would have to decide whether to follow what you suggested or not during special days in the life of the child as the child grows up amost let them know that you have a special role in their life, and during days like birthdays , performance maybe a musical performance day which the child is involved in or maybe a stage play that the child is acting you must make sure that you attend such events in order to show support for the child.
Another thing is that as a godfather your roles are limited , but majorly you are acting as a backup to the parent or for example when the child is becoming a teenager and needs someone to talk to apart from the parents, then you should definitely be there in their life to guide and support them, now back to the baptism you don't need to do anything much rather than to show up for the baptism , provide the maiden name which will give the child and support the parents at this period
Well the definition of a godfather has changed over time, but that's always with traditions, what has his source from the Catholic church. Basically a godfather should be named a god parent, and his origin is being a sponsor in Catholic teachings.
That is not a sponsor with money, but a sponsor in teaching the Catholic ways if the parents don't succeed in that job. There for a Godparent must be a Roman Catholic. So it latterly has nothing to do with money, or taking over parenthood from the parents, and more with sponsoring and guaranteed to the teachings of Christianity if the parents neglect that.
That has changed over time, in being a godfather who will help or support the parents if they lack of money or resources for there kids.
So i don't think they want you to be a Catholic teacher for their kids, and have something else in mind, and there for it would be good to ask them what they want you to be, or what to wear, and what kind of principles you need to know.
Like you said before, you are not a believer and there for it's needed to understand the facts about this subject.
And the truth is, a baby should not be baptized, only a adult who had chosen willingly to accept the Christian faith, because baptize is that someone accept Christianity.
But a baby or a child is not aware of the truth yet, and there for could not choose what to believe, and that also was changed over time.
Like Jesus was baptized when he was 30 and not as a baby or kid! But hey don't mention that before the baptize or you will ruin the party, and you will be the demon for ever! So maybe after a couple of months you can talk about this subject in a rational way.
The real truth that children or baby's get baptized is that we learned that from the older generations, and we could say, yes they had no options to find the truth. But we now in this time zone with all the information on the internet, should use that to find the true meaning or origins of traditions.
Or else we might hold traditions or values or principles what had nothing to do with the original meaning of some activities.