Immortality in the past was not always thought of in a physical sense - but in a spiritual sense. I think this concept of having a body that will be timeless and not give the appearance of aging came to the public when Hollywood got a fantastic grip on it.
Immortality today is not achieved in a physical sense either. What most people strive for with immortality is for their consciousness to live on after the body has decayed and withered. And this is perfectly capable of happening, and I believe that it happens all the time - even without a spell. The hopes of immortality is to preserve your consciousness (memory's, and relationships, and experiences).
To be honest, it sound a little self-centered in thinking. But who am I to judge what a man or woman wants to do with their life, or consciousness after their body has decayed.
The best way to extend your physical body's life is to treat it right, well, and to feed it properly. Make sure you are getting the rest you need, make sure you are cleaning yourself when it is necessary, and make sure you are eating foods that nourish and prolong your life.
I have a saying, "Nothing is forever", which is entirely true. People can't live forever. Cells divide and die, as we are biological organisms, we are bound to the physical laws of time and nature. Everything decays and dies someday. Luckily, the average human lives until about 75 now, so you have a long time ahead of you from that date of death. If you treat your body well, you can get an extra 20-30 years out of that number.
In short, immortality in the physical sense is not going to happen. Not unless you were traveling at the speed of light, or perhaps if some scientist out there got frankenstein weird and spliced the dna of a lobster with a human's. I hear lobster's live forever, so...