How can you separate homogeneous mixtures?
In a number of different ways, depends on the components of the mixture that you are trying to separate.
You can do
(1) precipitation/crystallization reactions - if one of the components can form a solid salt when the solution undergoes several factors (concentration change, temperature change, etc); separation can be done either by filtration, centrifugation, or simple decantation.
(2) chromatography - separation can be based on the mobility of the phases (liquid chromatography, gas chromatography, ion-exchange, etc.)
(3) solvent extraction - if the components are both liquid, separation based on their relative solubilities
(4) distillation - separation based on different boiling points.
(5) magnetic separation - if one of the components have magnetic properties.
(6) electrophoresis - separation of organic molecules based on the type of gel used
These are just some of the ways. Some can probably add more in this list.