It can depend on the type of lung cancer.  Small cell lung cancer is often not treated with surgery due to the fact that most times when it is first diagnosed it has already spread beyond the lung and therefore surgery would normally not be beneficial and the other modalities of radiation and chemotherapy would be used.

Non small cell lung cancer is the one most often treated with surgery although it is also treated with other modalities as well.  It is a decision made between you and your Doctor.  There are three common ways to utilize surgery for lung cancer and these are removing a section of the lung, a lobe of the lung or removing a whole lung.

Removing a section of the lung is called either a wedge resection or a segmentectomy.  A wedge resection is the removal of part of one or more lobes.  A segmentectomy is the removal of part of the lung along with the veins, arteries, and airways of that part.

Removing a lobe of the lung is called a lobectomy.  This is the most common type of surgery on the lung.  Removing two lobes is called a Bilobectomy.

Removing a whole lung is called a Pneumonectomy.

This should not be taken as medical or surgical advice and is a decision made with your own physician or cancer specialist.

Okay...first I need to begin with my classic disclaimer: I am not a medical professional so please do not construe anything I say as medical advice.  For a more detailed answer that takes into account individual circumstances one must see a doctor.  In light of this, I will do my best to answer you question : )

I am not exactly sure what you mean by the "classical" surgical approach, so I will describe the three most common.

1. Wedge Resection: This is where the cancerous tissue is removed, along with a bit of healthy lung tissue (for good measure.)  Though the risk of the cancer returning is higher for this method, it is also the one that has the lowest impact on your overall breathing capacity.
2. Lobectomy: The right lung consists of three "lobes" and the left two (or maybe it's the other way around...i don't recall); a lobectomy consists of removing the entire lobe.  This reduces your breathing capacity but is more likely to "get" the cancer.
3. Pneumonectomy: This involves removing the entire left or right lung.

HERE is an picture that will give you an idea of the above terms.  In surgery the cuts are made almost on you side...this way the doctor avoids going through the chest and getting near the heart.