The choice to ford a river or float across it like a boat was essentially a gamble among the depth of the water, the speed of the current, and the supplies at hand.
If the river appeared shallow enough and had the reputation for being so at that time of year, fording was the preferred choice. The river would be treated almost like another part of the land trail, albeit a capricious and potentially deadly one. The oxen would remain attached to the wagon and, well, walk across the river pulling it. Typically, someone would walk beside the oxen to steer them. It's important to keep in mind that covered wagons were nominally waterproofed from the outset, covered in tar on the bottom. However, diaries and memoirs from overlanders tell us about some of the hazards. If the river ended up pitching a sudden deep spot, the wheels would follow it down, and water would flood in over the sides! Jesse Applegate, who traveled with his family in 1843, tells of one particularly terrifying crossing. The river was too shallow and moving too fast to float the wagons across; their weight rode them too low in he water. But the current would surely wash them downstream to death. As Applegate writes, the only way across was safety in numbers. They lashed all the wagons in their group together, front to back. If one wagon lost its footing, it would be held in place by the others.
Where the river was too deep for oxen to walk and wagons to rumble, it was typically time to caulk the wagon and turn it into a temporary boat. In 1852, Ezra Meeker, his family, and the rest of their party got caught in a bottleneck of wagons poised on the Snake River near Salmon Falls. The crossing was daunting. One hardy group proved it possible. They tied three wagons together, unhitched the oxen, and just went for it. Some people swam with the oxen across; others rowed the wagons across against the current. Meeker found this inspirational or at least, he foud the ropet of saving the money that group wanted to charge to help him out, quite...motivating. "Oit came all the old clothes we could spare," he wrote later. "Out came the tar buckets, old chisels and broken knives. They stuffed scrap cloth into creaks and crannies in the wagon and tarred over them. I've read that some groups mighht cover the outside in animal skins if they had any, but Meeker doesn't mention that here (and when Applegate writes about actually building boats, they are just wood).
For those of you in this thread because of all the times you watch Mary Beth die of snakebite I'll finish up with one more detail. Safely across the river with his family, Meeker rode out to scout the trail. At the next river crossing, while he waited for his party to catch up, he established his own little temporary business. He boughht a wagon bed for cheap off a group who had decided to build boats and sail their things doen the river (which, Meeker notes, ended in "some deaths"). A little bit of work on the wagon bed, and--for the next few days, new arrivals could ford the river, caulk their wagon and float across, or hire a ferry to take them across.
you have died of dysentery
Come on, guys. This is a question about history, not everyone's favorite edutainment video game. Joke answers will be removed and warnings or temp bans issued.