Sandra is right. The reason you would tuck your head to your chest is to avoid making a direct pathway to your lungs for the pills to follow. By tucking your head, you close off your airway - sort of - and by tilting your head back, you "open" your airway.
That said, I have about 55 years experience taking pills on an almost daily basis. In addition to being a registered nurse, this makes me somewhat of an expert.
I am probably not the average pill-taker because I am so accustomed to taking pills. My dad remarked to me that he was amazed at my pill-taking ability!
What I do is place the pill on the back of my tongue and chase it immediately with a few drinks of water. Water really is the best fluid for taking pills with - soda can dissolve the pill before it reaches your stomach, potentially leading to irritation of your esophagus, and milk may be contraindicated with certain medications.
You can also disguise pills in a bit of applesauce as someone suggested. This is the way pills are administered to the elderly or mentally disabled in nursing facilities. Other things you can place your pills in include peanut butter (I use this for giving my dogs pills), ice cream, pudding or yogurt.
If the taste is offensive, give yourself a treat afterwards such as a piece of candy or spoonful of something tasty.
If your pills are scored, that is they have a line on them for cutting them in half, you can cut them in half or break them in half to make them smaller, but do not do this with pills that are not scored or with capsules.