Pathfinder does not use the 4th ed rule that a diagonal move is the same as a horizontal or vertical move. Instead, the rule is:
Oh, rather than the abstract “squares”, we say “five foot”, so the rule is:
The effect of this is that bursts and ranges have a much more natural looking circular shape (actually, it’s a slightly wonky octagon, but whatever).
So, no more square fireballs.
Lets say you have a 30′ move. If you are moving in a straight horizontal line, you count off the distance:
“five, ten, fifteen, twenty, twentyfive, thirty”
If you are moving in a diagonal line, you count it off like so:
“five, ten-fifteen, twenty, twentyfive-thirty”
If you are moving along a path to get around an obstacle, well, you have to keep track of whether your previous diagonal move was five or ten. But jeez – it isn’t all that difficult!
Spell areas of effect – bursts and blasts – are similar. A spell is taken to originate from a grid line intersection, not from a square. This means that a “radius 5” spell hits 4 squares.
The template for bursts looks like this. Note that the horizontal cone shape is slightly adjusted, but otherwise it’s pretty normal.
For line effect spells, you nominate an intersection on the foundry of your character (for normal size characters, that means on of the points on your square), an end point, and we draw a line.