To choose a separation method, ask what is different about the components of the mixture. The useful properties are solubility, boiling point, and whether a substance is magnetic or coloured.
If one component is an insoluble solid and the other is a liquid, use filtration. If the mixture is a solution and you want the solvent back, use simple distillation. If you want the dissolved solid, you can heat the solution to evaporate some of the water and leave the solid to form crystals. This is called crystallisation. If the mixture is two or more miscible liquids with different boiling points, use fractional distillation. If the components are soluble coloured substances, such as the dyes in a felt tip pen, use paper chromatography.
Some mixtures need more than one step. To separate sand and salt, add water so the salt dissolves, then filter. The sand is the residue and the salt solution is the filtrate. The salt can then be recovered from the filtrate by crystallisation. Iron filings can be separated from sulfur powder with a magnet, because iron is magnetic and sulfur is not.