There is a good history and summary of the rules of Barbu on this Pagat page. However, it's not the rules I'm used to playing (nor do they sound like they will play as well). Here are some differences in our play:
Terminology:
"No Tricks" = "Nullo"
"No Queens" = "Queens"
"No Last Two" = "Last two"
"No Hearts" = "Hearts"
"No King of Hearts" = "Barbu"
"Dominos" = "Fan tan"
Scoring:
Barbu scores -15 in ours; -20 in theirs.
First Fan tan finish is 40 in ours; 45 in theirs.
Play:
They have no "must play" rules, except must over-trump always applies for them.
For hearts, we allow a hearts lead after hearts have been broken.
Dealer always leads in our rules; dealer's left in theirs.
Dealer chooses the game in our rules; dealer's left in theirs.
We have no "must double" rules.