Why should I fear death?
If I am, then death is not.
If Death is, then I am not.
- Epicurus
For Epicurus, 'life' is a sensory experience. Death is the absence of sensation, and therefore it is not a feature of life.
But, you may argue, death is not simply the absence of sensation, it is also the *cessation* of sensation.
Well, to worry about that points us to another problem.
Let's try to think about our sensory experience as a kind of waveform or signal. Our general experience will have a 'baseline' or 'natural' waveform. The shape of this waveform is dictated by our bodies and their interactions with the natural environment. For example, when the light changes due to the motion of the sun, we may begin to feel more or less sleepy. When we work, our bodies use-up energy and we feel the need to eat. Our natural signal does fluctuate, but the fluctuations are patterned, periodic. Like the patterns of the seasons there is a regularity and familiarity to them.
However, beyond these 'natural', periodic variations in sensation, we have found endless ways of modulating the signal. Imagine gorging on a particularly delicious piece of cake. All of a sudden, our baseline waveform spikes higher than we ever could have imagined. Soon, it returns back to its natural baseline and we feel dissatisfied. We crave another piece of cake to stimulate our sensations again. But, this second piece doesn't modulate the signal quite as much as the first one, so we feel even more dissatisfied.
Fast-forward hundreds of years of 'modern' civilisation and our daily 'natural' baseline is totally corrupted. We are constantly bombarded by signals that modulate and stimulate our sensations. If we're materially fortunate, we can continue to artificially stimulate our pleasure and avoid really 'coming down'. Eventually, though, something puts and end to all this noise - death. This is why we fear death today. Not because of something intrinsic about death itself (after all, it is a natural, essential feature of biological milieus), but because it signifies an end to our enjoyment.
So, learning to not fear death means also learning to pay more attention to how we experience pleasure in life. As I said, our natural signals are periodic, like sine waves, (as opposed to the 'noise' signal of artificial stimulation), pleasures come and go. We feel hunger. This hunger can be satisfied by anything which eases this hunger - a simple slice of bread. Then, our hunger disappears, and returns again later. In which time we can again enjoy the bread. Accepting these cycles means accepting their end too.
Finally, when it comes to a question of the many forms of natural, extreme suffering we will still encounter, such as periods of illness, Epicurus says that nature has also provided a faculty to counter-balance these kinds of suffering - memory. In times of illness, Epicurus encourages us to remember and reflect on the good times we've spent with friends and family.