You stop, analyse the situation, and look for a better way around.
From your question it's more about standing water on the road. I would avoid riding through any water where I can't see the bottom. Water should be relatively clear on a sealed road, but on a dirt road it will likely be clouded.
Do also remember that riding over wet ground will damage it. By getting off and walking, you're spreading your weight over more surface area and improving you traction.
Since you had local knowledge of the likely depth and condition of the bottom, and you could visually see the flow rate, then you could make an informed decision whether to proceed.
If you were in the same situation without fore-knowledge, and you know there's no other way around, then same as a 4WD crossing a river, you walk the route first unencumbered by a bike and gear.
All the time, you're considering what you know and what you're learning.
If the water is flowing, then you risk being washed off your feet/wheels and potentially downstream. If this is remotely possible, you get out of the water and reevaluate.
Ultimately, if you have doubts about crossing, then don't. Either back off and wait for the water level to drop, or find another way around.
Based on the new picture, you're asking about wet roads. To expand on that:
Just avoid the puddles where possible. Stay on the drier visible surface, and look ahead to avoid getting boxed-in. These puddles are shallower at the edge, so aim to avoid the middle and just skirt them if you have to.
This is wet mud and will be horrible to ride in. Find another road/path ideally, but if you ride this expect to sink in and stick. With no forward momentum you will fall sideways and have to put a foot down, which will sink and possibly throw you into the mud. Not ideal.
Look at the sides and see if there's firmer land there. Avoid crossing a fence onto private land where possible.
Ford This is a formed river crossing that isn't a bridge. There's a concrete surface visible through the water (sometimes this is just a strip of gravel)
and poles to show the exit point on the far side.
This water is flowing from right to left, so cross on the upstream side as long as the flow rate isn't excessive. These crossings are unsafe when the river volume/flow rate is high, and they can be bone-dry in the summer. Smart road users will only have one vehicle in the water at a time, and absolutely never going in opposite directions.
In my country, these have been blamed for spreading Didymo weed across catchments, and are only seen in rural areas.
Not so much water here today, but imagine if it was wet. The rutts would fill in first, hiding their depth and the rocks in the right side. On a bike I'd take the middle island but that runs a risk of diving under water leaving me stuck on a narrow with nowhere to put a foot down.
So I'd prefer to be on the right bank passing left of the one rock.
Since its all dirt/mud any standing water will be murky.
If the water was high enough I'd get off, and carry the bike up the bluff on the left, or walk over the rocks on the right. But realistically, I'd be giving up and going home if the puddles were deep enough to submerge that motorbike.