Sorry, I posted the wrong photo. This shows how bad it can get.

Number One: You have to prevent the RUNOFF water coming to your garden area, by somehow redirecting it away (barrier, trench).
Number Two: dig a trench through the lowest part and lead ithe rain water away.

Number Three: Anothe option is to create an slope such that the runoff water wil flow away.

Of course, I have no idea how the lay of land/terrain is around your garden area.

On a drier occasion I would add soil to the bed where there is the lowest elevation. You can improve the drainage of the area by making it level throughout.

I agree with digging a trench around the area of the garden to redirect the flow of the water.

In my garden, I shovel the dirt from the trench to the left and right so that the rows have "drainage" between them and it sort of helps to raise to bed out of standing water.

I see that the left side of your photo is higher ground. Can you move your garden in that direction?

I see a downspout from your gutters dumping right next to the patio.

You could probably help things a lot by putting in a pipe to carry that water away.

Your neighbors gutters are probably contributing also. It would be a lot of work, but a French drain along that wall would probably work.

If you can't divert the run off to that location can you haul in dirt and raise the whole elevation of the yard? You'd have to grade it so it sloped away from the house and toward the fence line so that might mean building a low retaining wall of some sort on the outside edge of the patio/sidewalk. A landscape contractor can give you an evaluation, suggestions, and estimate - usually for free.

Dave

I think the garden is the lesser problem. That kind of standing water will rot out your fence before its time. Every home I've owned has been graded to remove water from the property, usually with sloping combined with french drains.