Do I need a feeding tube?
Only in specific circumstances. For most cancers, where the normal path of feeding is intact, and patients can eat and drink by mouth, it is not necessary. Even if you don't have an appetite or taste for regular food, or are hindered by nausea, your food intake can be supplemented by supplement drinks, ice cream and puddings. 
However, when the oral cavity or food pipe ( esophagus) is undergoing treatment, or has suffered permanent damage from treatments, that the placement of a feeding tube directly into the stomach can deliver liquid supplements, hydration and medication. This tube enters the stomach directly through the abdominal wall, and has a stopper which closes it off when not in use. Feeds are introduced into the stomach by pushing with a syringe, by gravity, hanging a bag on a pole, or via a pump, to deliver a constant amount over several hours. A nutritionist working with your oncologists usually guides you about the amount of hydration and calories needed. Many medicines come in liquid form, and can be introduced via this tube as well. 
Sometimes the stomach can feel bloated with the volume introduced at one time. Medicines ( metoclopramide) can help with improving forward flow; delivery via pumps overnight decreases the sudden inflow that bolus feeds cause.
For most patients getting treatment for head and neck cancer, this support is critical to get through treatment without getting malnourished and dehydrated. The tube is removable after the patient can maintain weight by oral intake. 
There are a few circumstances in which a feeding tube is a permanent solution. E.g. When some one has had a laryngectomy, or a voice box removal, the architecture of the swallowing mechanism cannot be reconstructed, and the feeding tube is a permanent solution. Or when the esophagus is obstructed, the feeding tube is the only way.
There are other ways to maintain supportive nourishment; these are alternatives not meant for long term support. At times , the GI tract is not functional, and intravenous feeding is the only option. Part of the reason that this is not optimal is that it requires a large bore catheter into a large vein, maintained for the exclusive purpose of alimentation. This then can become a nidus for infection, given the glucose rich environment. And, at the point when IV feeding is the only means of nourishment, one has to step back and question what the goals of treatment are, at that point. There are no right or wrong answers: I know someone who has been on IV feedings for more than one year, and he is inching his way towards getting his insides reconnected, and getting back to oral feeding.