The different stages of the method are lyse, bind, wash, and elute.  More specifically, this entails the lysis of target cells to release nucleic acids, selective binding of nucleic acid to a silica membrane, washing away particulates and inhibitors that are not bound to the silica membrane, and elution of the nucleic acid, with the end result being purified nucleic acid in an aqueous solution. 
For lysis, the cells (blood, tissue, etc.) of the sample must undergo a treatment to break the cell membrane and free the nucleic acid. Depending on the target material, this can include the use of detergent or other buffers, proteinases or other enzymes, heating to various times/temperatures, or mechanical disruption such as cutting with a knife or homogenizer, using a mortar and pestle, or bead-beating with a bead mill. 
For binding, a buffer solution is then added to the lysed sample along with ethanol or isopropanol. The sample in binding solution is then transferred to a spin column, and the column is put either in a centrifuge or attached to a vacuum. The centrifuge/vacuum forces the solution through a silica membrane that is inside the spin column, where under the right ionic conditions, nucleic acids will bind to the silica membrane, as the rest of the solution passes through. With the target material bound, the flow-through can be removed. 
To wash, a new buffer is added onto the column, then centrifuged/vacuumed through the membrane. This buffer is intended to maintain binding conditions, while removing the binding salts and other remaining contaminants. Generally it takes several washes, often with increasing percentages of ethanol/isopropanol, until the nucleic acid on the silica membrane is free of contaminants. The last wash is often a dry step to allow the alcohol to evaporate, leaving only purified nucleic acids bound to the column.
Finally, elution is the process of adding an aqueous solution to the column, allowing the hydrophilic nucleic acid to leave the column and return to solution. This step may be improved with salt, pH, time, or heat. Finally, to capture the eluate/eluent, the column is transferred into a clean microtube prior to a last centrifugation step.