Let's say I had a Death Note. If I wrote someone's name in the book and then wrote details of the death, can an individual stop the cause of death and the actual death entirely or will the death still take action, but in a different way?
The Rules of the Death Note are pretty clear:
As you see above, the time and conditions of death can be changed, but once the victim’s name has been written, the individual’s death can never be avoided.
This is, of course, as long as you thought of the victim’s face while writing the name. In case you now assume that you can just alter the details of death to something impossible, well sorry:
In the occasion where the cause of death is possible but the situation is not, only the cause of death will take effect for that victim. If both the cause and the situation are impossible, that victim will die of heart attack. [emphasis mine].
So again, all you get is a heart attack. The victim will die.
Tl;dr: Think before you write.
Rule XV states that
When the same name is written on more than two Death Notes, the note which was first filled in will take effect, regardless of the time of death.
If writing the same name on more than two Death Notes is completed within 0.06 seconds, it is regarded as simultaneous; the Death Note will not take effect and the individual written will not die.
So, if an individual is very, very fast he can save another from being killed by the Death Note (if you have two other Death Notes); this can happen as a very unlikely coincidence. But this rule states that "writing the same name (...) is completed within 0.06 seconds", so to save another life you need to write the name in the other two (or more) Death Notes soon after the name was written, and so before the causes of death.
So it's a task for The Flash... or maybe for Cyborg 009 since this is the Anime & Manga Stack Exchange.
Its not possible to stop the person dying from the written cause. The Death Note has no provision for avoiding death until and unless the writer doesn't have the person's face in their mind when writing his/her name.
In the occasion where the cause of death is possible but the situation is not, only the cause of death will take effect for that victim. If both the cause and the situation are impossible, that victim will die of heart attack. (Rules of the DeathNote. How to Use: LV)
So, hypothetically speaking, if an individual's name was written in the DeathNote and they were able to bring about events that would render the situation of their death impossible, they will still be susceptible to the cause of death.
However, there are no rules that specify what would happen to the victim of they were able to prevent the cause of death (be that if the cause was "shot through the heart" and the victim locked themself in solitary confinement for example). Though, knowing how the DeathNote rules go normally, the victim would probably just die of a heart attack.
The wikia contains a full list of all the rules regarding the use of a DeathNote.