As with all writing you need to consider the audience, what mesage you are trying to convey and of course, for non-fiction, what information you have.
I think some sort of genealogy program is pretty much essential for keeping track of your family and most of them can output data in various forms automatically.
I quite like Outline Descendent Reports where each new generation is indented further to the right. It is a very flexible form, unlike the conventional 'tree' arrangements which struggle when there are many children or multiple spouses.
For my greatgrandfather, grandfather and father I have written up 'timeline' articles which I have published on the web and emailed to family members who have expressed an interest in family history. If you do write anything on the computer it can be a good idea to save it in 'PDF' form as the chances are it will always be computer readable in the future, not necessarily the case with 'word processors' in general. Similarly material on the web is essentially 'plain text' so shouldn't become unreadable (as long as it doesn't get lost).
Unlike 'normal' writing I wouldn't worry too much about structure - the same applies to personal memories - just write it down as it comes! Editors are two a penny but source material is gold. Other people might comment on what you have written, building up the picture and removing errors. They can't do that if you haven't made a start.
There is no right way, do what suits you.
As well as the computer I keep ring-binder files. I like using polypockets. The generations are separated by tab sheets and each family starts with a Family Group Sheet behind which all the family papers sit. Spouseless children might have birth and death records here, married children get their own Family Group Sheet beyond the generational tab sheet. Again no right or wrong here. I give image files names like b8910jsh.jpg , b for birth 891 for 1891, 0 etc. to allow for potential conflicting files and jsh for, say, JohnSmitH. I was brought up in the days of 8+3 file names, nowadays one can be a lot more specific. My system does allow files to be easily grouped by date and type though.