How can I calculate the moles of solute?

Since the question is a little vague, I'll try and provide some clear-cut examples.

A solution is a mixture composed of a solvent - the substance that dissolves - and a solute - the substance that gets dissolved.

The easiest way of calculating the number of moles of any substance is by knowing its mass and, of course, what that substance actually is - i.e its molar mass.
So, for example, if 10.0g of sodium chloride are dissolved in water, all you need to know to determine the number of moles of solute is given to you

the solute - sodium chloride
the mass - 10.0g
its molar mass - 58.5g/mol
...............................................
#n = m/(molar.mass) = (10.0g)/(58.5g/(mol)) = 0.17# moles

This will represent your basic strategy - assuming you know what the solute is, always determine how much of it you have - its mass.

Let's say you have a 15.0% percent concentration by mass solution of sucrose dissolved in 250g of water. If you want to determine the number of moles of sucrose (#C_12H_22O_11#), you'd first determine how much of it is present in your solution. So,

#c = m_(solute)/(m_(solution)) * 100% -> m_(solute) = (c * m_(solution))/(100%)#

#m_(solute) = (15.0% * 250g)/(100%) = 37.5g# sucrose

So, knowing sucrose's molar mass - 246 g/mol, you'd get the number of moles

#n_(sucrose) = m/(molar.mass) = (37.5g)/(246 g/(mol)) = 0.152# moles

If you're dealing with molarity, the number of moles of a solute can be determined by

#n = C * V_(solution)# - with the volume and/or the molarity usually given.