So what happens when you buy the farm, kick the bucket, answer the last call and assume room temperature?
First, it's important to know the difference between death and unconsciousness. If upon entering a command it states you're unconscious, don't panic. You aren't dead. You may well wake up to continue RP, run from a fight or whatever you consider wisest.
Once you see the red scroll (you'll know it when you see it), you're dying. Still, no need to panic - there's a certain amount of time between taking a mortal wound and dying in which you can be revived by a qualified medic. Therein lies the importance of having in-character friends.
What happens once you're past the revival window? If you had the foresight to purchase a clone, you'll be faced with one choice: you must go to your waiting clone body and be spewed forth into the world once more.
Once you clone, you'll only have memories (and stats/skills!) up to your last clone update so roleplay accordingly. There is only one exception to this: You can be brought to a cloning facility and dumped in a recombinator which will forcibly put you into a clone body. This is feasible even if you haven't purchased a clone. In this case your memories of the last 24 hours should be hazy due to brain damage; the last hour before your death, much more so. You will not remember the death itself and the events immediately leading to it.
Keep in mind that it will take some time for you to reach the cloning choice area. This is a good time to have a drink and calm down - getting killed can rile up OOC feelings sometimes and it's best not to enter the world again until you feel you can roleplay it properly.