What is the best way to create personal backup copies of dvd's of home
movies and dvd's (Not Mainstream)?

If there not mainstream then there isn't ,uch you have to worry about.
It all depends then on if you want to be able to reburn them onto
other dvd's or vcd's or if you want to add titles and such to the
disk.

If you're looking to simply backup a home-brew DVD, it's most likely
already burned on a 4.7GB DVD+R or DVD-R disc. Copying such a DVD is
as simple as copying a CD; use your favorite disc burning software and
use its copy disc option.

These sites have good articals on exactly this.
http://www.videohelp.com/dvdbackup
http://www.afterdawn.com/guides/archive/full_dvd_to_dvdr_with_clonedvd.cfm


You might also want to read my comment on the folowing question.
http://answers.google.com/answers/threadview?id=469000

Use free software such as dvd shrink, or there is loads of advice and
collections of software on www.doom9.org

http://www.shrinkdvdz.com has all the software that you need to copy,
decrypt DVD for backup purposes.  You can even shrink a full length
movie to fit 1 standard CD-R disc.