I got married this year and my best man did a great job, so I'll share my experiences.
My wife and I didn't need much support in organising it, so my best man was pretty redundant up until the week of the wedding (stag do aside).
In the week leading up to the wedding he was really supportive, helped with little things like picking up the suits, carrying boxes of booze about, wrapping little bloody chocolate hearts. He also returned the suits for the whole wedding party whilst I jetted off on honeymoon.
On the day the band needed directing and paying, also the photographer needed paying, I let him handle all the cash for that so I didn't have to worry about it. He was also main point of contact for all the other suppliers (venue, caterer, driver etc), so it was important that we walked him through all the plans and running order in advance and gave him the contacts.
On the day he went above and beyond with chatting to all our families, dancing with grandma's, downing jaegerbombs with father in law etc etc.
He took a few days off from work to be around for all that, and also just to be around so I had someone to hang out with in the downtime and not stress too much about things.
Of course the speech and the stag do are important, but it is the rest of it where the best man really makes a difference.
Ask what the groom expects of you, but he probably won't know so just being around and available as things come up is a good start.
