What volume of a 0.25 m phosphoric acid solution is required to react completely with 1.0 l of 0.35 m sodium hydroxide?

The moles have to be equal. Always start with a balanced equation. This reaction is a double replacement.
The basic equation is
NaOH + H3PO4 ===> Na3PO4 + HOH

The balanced equation is.
3NaOH + H3PO4 ===> Na3PO4 + 3HOH

moles of NaOH = moles of H3PO4
mols of NaOH = molarity * Volume
molarity = 0.35 mol/L
Volume = 1.0 L
moles NaOH = 0.35 * 1 = 0.35 mols

Find the moles of H3PO4
For every mol of H3PO4 used, you require 3 mols of NaOH
3/1 = 0.35/x
3x = 0.35
x = 0.35/3
x = 0.1167 moles of H3PO4 needed for this reaction.

Now the volume needs to be calculated.
n = 0.1167
M = 0.25 mol/L
V = ??

Formula
M = n/V
V = n/M
V = 0.1157/0.25 
V = 0.467 L

Note: I merely copied the reaction given myself to the next line. I'm not copying from an outside source.