Cigar smoke is not inhaled into the lungs. The smoke is drawn into the mouth, held briefly so the palate can read it, and then exhaled. This is the most important technical difference between cigar smoking and cigarette smoking, and it is also the difference that produces the entire pleasure of the practice.
Cigarette tobacco is engineered to be inhaled deeply because cigarette nicotine is delivered to the bloodstream through the lungs. Cigar tobacco is fermented, aged, and rolled to deliver flavour through the mucous membranes of the mouth and the retronasal passage; the nicotine that reaches the bloodstream does so through the mouth and throat lining, more slowly. Inhaling cigar smoke not only fails to produce the experience the cigar was made for, it produces an unpleasant, harsh, often nauseating effect.
Once the smoke is in your mouth, two motions are useful. First, simply tasting: rolling the smoke around the mouth to identify the flavours on the tongue, the soft palate, and the gums. Second, retrohaling: gently exhaling a small amount of smoke through the nose rather than the mouth. The retrohale exposes the smoke to the olfactory receptors in the nasal cavity, where most flavour perception actually happens, and reveals notes that the mouth alone cannot read.
For more on cigar fundamentals, see The Anatomy of a Cigar.