A river crossing is the most extraordinary thing most people will ever watch, and it is genuinely not something anyone can book for you.
Two rivers, two different things
The Grumeti, in the western corridor, roughly late May to July. Smaller, narrower, and known for very large crocodiles. Crossings here tend to be shorter and less chaotic than the Mara, and there are far fewer vehicles watching.
The Mara, in the northern Serengeti, roughly July to October. The one in the documentaries. Wide, steep-banked, and the herds cross back and forth repeatedly rather than once, so a single area can produce crossings over weeks. It's also where almost everyone goes, so popular crossing points get busy.
Why it can't be scheduled
Wildebeest gather at a bank in their thousands, wait, mill about, and then either go or don't. They can stand there for six hours and walk away. Something as small as a vehicle parked in the wrong place can turn a herd around. Then an hour later they'll cross somewhere else entirely, with no warning at all.
Giving yourself a real chance
Be there in the window. August and September are the safest bet for the Mara, late June and July for the Grumeti.
Stay close. A camp within reach of the river means you can be at a gathering point at first light. An hour and a half away means you arrive after it happened.
Give it three or four nights. One night is a lottery ticket. Four nights in the right place in the right month is a good chance, and still not a certainty.
Be willing to wait. This is the hard one. Seeing a crossing usually means sitting at a riverbank for hours with a packed lunch, doing nothing. People who need to keep moving miss them.
What it's like
Loud, dusty and fast, and more upsetting than people expect. Animals drown, calves are separated, and crocodiles do what crocodiles do. It's not a show. Most people are quiet afterwards.
If it doesn't happen
Then you spent four days in the northern Serengeti in the company of enormous herds, big cats following them, and some of the best scenery in Africa. Anyone who sells you a crossing as a certainty is selling you weather and animal behaviour, neither of which is theirs to sell.
Behaving at a crossing
Engines off, voices down, and stay in the vehicle. A herd that has spent two hours working up to the bank will turn around for a slammed door or a vehicle parked on the crossing line, and then nobody sees anything. Your guide will position well back and side-on for exactly this reason, and a guide who pushes to the front is spoiling it for forty other people.