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In what circumstances would cover affect melee attacks?
If three characters are lined up as shown in the diagram, and the bottom-right man in armor makes a melee attack against the frog creature in the upper-left (through the woman's square, and around the corner), does the frog have half-cover from the attack?
Unless otherwise state by some specific ability (i.e. sharpshooter)
I'm going to steal a fair amount from my answer about reach weapons and cover here, as I think it's mostly the same.
With that in mind we can evaluate whether or not an attack from some position incurs cover from another position.
Cover
Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an attack or other effect originates on the opposite side of the cover...
... A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a ... creature, whether that creature is an enemy or a friend. (emphasis mine)
p.250 and p.251 of the DMG have a chart/description.
To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker's space... trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover....
So, we can attempt the same exercise with your image and we see that if either the woman or the wall were not there, no cover would be gained. Since both are present, the target receives a bonus for half cover.
The rules for cover are below:
Cover
Walls, trees, creatures, and other obstacles can provide cover during combat, making a target more difficult to harm. A target can benefit from cover only when an attack or other effect originates on the opposite side of the cover.
There are three degrees of cover: half cover, three-quarters cover, and total cover. If a target is behind multiple sources of cover, only the most protective degree of cover applies; the degrees aren’t added together. For example, if a target is behind a creature that gives half cover and a tree trunk that gives three-quarters cover, the target has three-quarters cover.
Half Cover
A target with half cover has a +2 bonus to AC and Dexterity saving throws. A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend.
Three-quarters Cover
A target with three-quarters cover has a +5 bonus to AC and Dexterity saving throws. A target has three-quarters cover if about three-quarters of it is covered by an obstacle. The obstacle might be a portcullis, an arrow slit, or a thick tree trunk.
Total Cover
A target with total cover can’t be targeted directly by an attack or a spell, although some spells can reach such a target by including it in an area of effect. A target has total cover if it is completely concealed by an obstacle.
I'd consider the corner of the wall to be blocking at least half of that creature (it might be Bullywug) so it would get half cover from the attacker in the lower right.
I will also note that a melee attack victim could have cover if the attacker is attacking with a reach weapon and there is a creature between the attacker and the target.
