Diluting a solution adds solvent without adding solute. The number of moles present does not change; only the volume they are spread through does. That single fact gives the dilution equation.
The units of concentration cancel, so molarity, percent or grams per litre all work — as long as you use the same unit on both sides. The same is true of volume.
Making it up correctly
Measure the stock volume accurately with a pipette, transfer it to a volumetric flask, then add solvent up to the graduation mark. Do not measure out the solvent separately and add it to the stock: volumes are not always additive, and the error compounds with the concentrated solutions where accuracy matters most.
Serial dilution
To reach a very low concentration, dilute in stages. Ten successive 1:10 dilutions give a factor of 10¹⁰, which no single step could achieve accurately. Each stage carries its own error, so mix thoroughly between steps and use a fresh pipette tip each time.
Safety with concentrated acids
Always add acid to water, never water to acid. Dilution releases a large amount of heat, and adding water to concentrated sulfuric acid can flash it to steam and eject acid from the container.