How to change width/height of selection using keyboard in Photoshop?

To make a "perfect" size selection you could do two things.

1st ...Thing

1. Make the selection ( can be quite halfassed selection )
2. Make a Quick mask ( Hotkey: Q )
3. Activate Free transform ( Hotkey: Ctrl+T )
4. Expand the selection to the dimensions you need.
5. Accept Free Transform ( Enter or double click inside Free transform )
6. Hotkey: Q will get you out of Quick mask.

This is also good just for the sake of snapping.

It might seem like many stages but everything together except 4. can be done in few seconds.

Now that I'm back on my pc, here's informational image:

2nd ...Thing

1. Make the selection ( So that you'd rather have extra than less than you need )
2. Fill the selection with a color ( Reduce opacity if needed )
3. Make another selection ( You can nudge that selection around with your arrow keys and Delete extra off. )

Yes you can change the selection by an equal number of pixels in height and width,

Go to select->modify->Expand(to increase)->Contract(to decrease)

You can also follow this for exact size marquee selection :

In the snapshot below (which shows the options palette when the selection tool is active) you'd pick "fixed size" style and then enter your desired width and height in just next(width height)box.

I am unaware of a way to "nudge" the size of the selection. However, the info palette shows the size of the marquee, and you can then use that information to determine and then manually key in the values you want.