The construction of bridges becomes possible in the Neolithic, after unlocking the stilting tech.
They are very useful for allowing your villagers to cross rivers, allowing them to hunt more easily and access scarce resources such as mines and megaliths.
Building the bridge
To build a bridge, you have to click on one side of the river near the water and hold the click down to the other side of the river. If you start your bridge too far from the water, the game will tell you that it is impossible to build it.
You will need 1 log for each length square. There appears to be a maximum of 10 squares for the length of the bridge.
Building a good bridge for the mobility of your villagers, but raiders will also use it to attack you.
Knowing this, do not hesitate to add a door and guard towers near the entrance of your bridge to have a defense and be well prepared for attacks.