what method should be used to separate the mixture of water and vinegar?

Water and the acetic acid (ethanoic acid) in vinegar can be separated by fractional distillation. The boiling point of water is lower than that of acetic acid. Therefore, water is fractionally distilled off first, and then acetic acid.

Distillation

fractional crystallisation

General methods of water-organic mixtures separation like distillation and pervaporation can be used.
Another method to separate water from acetic acid is based on azeotropic mixture formation with water.
The requirements for the solvent should be as follows:
1. It doesn't mix with water solutions
2. Azeotropic mixture's boiling point is lower than waters (100 degrees)
3. Acetic acid should be much more soluble in water rather than in azeotropic mixture.
This method can help to perform separation at lower temperatures than in regular distillation, but requires a lot of organic solvent.
As an example, buthylacetate or dichloroethane can be used.

fractional distillation might work if there is enough of a difference between boiling points.