I generally pay for all expenses on my cards and cash and write
everything in a small book at the end of each day.. I even go over with
my friends and ask them if I missed anything.

I even note the amount I lend them for shopping or other expenses that
are not common. (Generally they don't ask me for shopping cash)

At the end of the trip, I do all the calculations and email everybody
the overall expenses and their share.

In several years of traveling with friends, I've never been short changed.

Also keeping a daily tab on the expenses keeps you from blowing your
budget.

It helps to have one cashier on the trip. Its easy to keep track
of the expenses.

Hope this helps.