You can find practical information from Qiagen website if you use their kits which are quite popular these days.

It depends on which methods you use for isolation. The alkali lysis (see link below) was commonly used to rupture bacteria. Plasmid DNA (smaller in size and more soluble) is separated from baterial genomic DNA (larger and less soluble). The plasmid DNA is then separate from proteins by phenol extraction where the proteins are removed to the phenol phase while plasmid DNA stays in the aquous phase. The plasmid DNA is then precipated with ethanol to complete the purification.

Qiagen’s kit and others overcome the use of phenol (which is toxic and smelly) by using a solid phase that bind DNA to seperate the contaminating proteins. The DNA is later eluted from the solid phase to complete the purification.

Here are additional links:
http://biotech.biology.arizona.edu/labs/DNA_isolation_plasmid.html
The concept of alkali lysis method of plasmid DNA isolation is shown here:
http://a32.lehman.cuny.edu/molbio_course/plasmid_protocol.htm