I feel your pain mate. I was my brother's best man (going back 10 years or more now) and was shitting myself about the speech for weeks beforehand.
First off - it doesn't have to be War & Peace. People are surprisingly receptive if you keep it quite short and snappy. Mine lasted 4 or 5 minutes at the absolute tops.
Open up with a little bit of background about how your brother and his wife to be met. Try to find an amusing - but not too risque - anecdote or detail about their dating days. I found an old Valentines card that my brother's wife had sent to him when they first started going out and that provided enough material for a couple of minutes at least.
From there go into the "serious" part about how much they love each other and how it was obvious from the start that they were always meant for each other - yeah, it's a bit corny, but if you keep it brief and say something nice then people will appreciate it. Then from memory I think you thank the bride's father and/or the bridesmaids and toast the bride & groom. Also, if there are any telegrams or messages from people who can't attend, these all take up a bit of time.
As I say, it was a long time ago and I'm a bit fuzzy about the details, but the best advice is not to fret too much. People aren't expecting Bill Hicks to turn up and deliver a stand up masterclass - just a bit of humour (it's a wedding, people are drinking and want to be polite, so they will laugh at most things that are meant to be funny, even if they aren't), a bit of serious "nice" stuff, and then onto the formalities.
Good luck, I'm sure you'll be fine.