Building bridges on river consists of 2 stages namely
1: Under-earth(water) construction
2: Above earth(water) construction
The second stage is a bit easy compared to the first as it is the same as other bridges/flyovers on the ground are built.
So, first lets know how the sub-structure(under water structure) is built.
The foundation is generally of pile type which means, bore holes are drilled. From these bore holes the water are drained off and the hole is cased with steel. After this the concrete is poured into it. Two(or even more sometimes i.e, like a group of piers) piers of such type are constructed then , a temporary wall like thing with bamboo or steel around them of some area is constructed and the water between them is removed. After this, the gap is filled with sand and concrete, the concrete used is of rapid hardening type which means , the concrete gets hard as soon as it gets in contact with water. After this, the foundation like thing which will be above the water is constructed on top of this.
Now, The pillars(columns) are raised on them. With this the foundation part will be completed similar thing is done all along the span the bridge is planned.
Now the remaining part is the super structure, i.e, the deck of the bridge. Now a days, pre-fabricated ducts are used. These are arranged in between the pillars from one bank to the other. Thus the construction of a bridge on a river is completed.