You won't find them on regular paved roads or even gravel rounds, and off-road driving is illegal in Iceland. You'll only find rivers to ford on the F-roads (jeep tracks). And you can only drive on F-roads with a 4x4 hire car. Here are the key tips for fording a river:
1. Locate the tracks on either side of the river, to find the entry and exit points.
2. If you can't see any tracks, focus on faster-flowing (shallower) water.
3. Check the depth first by watching the car in front. If there isn't one, wade across.
4. Turn off the headlights and tail lights.
5. Make sure the car is in 4x4 mode and (if you can) lock the inter-axial differential.
6. Keep the car in a low gear (first or second). If it's an auto, switch to manual mode.
7. Proceed across the river slowly and steadily. Do not stop, brake or change gear.
8. Once on the other side, if you stop, do not switch off the engine. Let it dry off. https://www.nextstopiceland.com/driving