Mixtures are all able to be separated by exploiting some physical property. No chemical changes need be involved, so the substances will retain their chemical identity throughout the separation process.
I. Hand Separation
An example which could be separated by hand might be a dry mixture of salt and sand. Manually picking out the sand does not change the chemical identity of the salt or the sand.
Even though this technique is crude, it does show up in making an important discovery. It was the discovery of optical isomers by Louis Pasteur in 1844, the first major discovery of his scientific career. He was able to separate what had been thought to be one compound into two. He carefully crystallized the compound and, the key insight, saw that that it crystallized into right-handed and left-handed crystals.
He able to pick out the opposite handed crystals and demonstrate that solutions of each rotated polarized light in opposite directions. It turns out, for a number of reasons, that Pasteur was very lucky. However, notice that he DID see that luck had presented something important to him and he was able to follow it through.
II. Filtration
Filtration is a bit more sophistication than manually picking out stuff. Mix the sand/salt with water. The salt dissolves, the sand does not. Pour through a filter to separate the sand, then heat the salt water to drive off the water. All physical changes.
Often, in chemistry, a reaction will be carried out and a solid material formed where there was none before. Filtration is the most common technique to remove the solid material.
Filters range widely in sophistication. Common ordinary filter paper (as might be used to make coffee) is inexpensive. The filter used in an oil filter for a car costs a bit more and so on. There are special application filters in various areas, both chemistry and other, where the filters are quite expensive.
Sometimes, the solid portions is what you want and sometimes it is the material you discard, keeping what passed through the filter. In 1943, Glenn Seaborg discovered element 94, later named plutonium. He and his co-workers carried out a series of steps, both chemical and physical, to purify the plutonium, one of which was a filtration. They kept the solid and discarded what passed through the filter.
Sometime later (2-3 years? I'd have to check), Seaborg discovered that elements 95 and 96 were also in the samples prepared. However, they were soluble, stayed in solution, passed through the filter and remained undiscovered due to the then single-minded focus on plutonium. (Plutonium was used to build the first atomic bomb and was also used in the bomb dropped on Nagasaki, three days after a uranium bomb was dropped on Hiroshima.)
III. Distillation
Imagine a solution of alcohol and water. Heat it. The lower boiling component (alcohol) will come off first, so you hold the temperature until all the alcohol is gone. You've separated the water and the alcohol with only physical changes involved. (The actual technique is a bit more sophisticated, but you get the idea.)
IV. There are more
There are a number of other separation techniques which exploit physical properties. Examples include:
centrifugation
chromatography
gaseous diffusion
zone refining (a ChemTeam favorite!)
An interesting one is an air column separator. Suppose you are asked to separate a mixture of salt and pepper without doing it by hand. An air column separator would work, as well as dissolving the salt (pepper does not dissolve in water). By the way, air column separators are used to clean and separate seeds. Many botany programs maintain seed banks. An air column separator is used to "purify" the seed sample before long-term storage.