It's quite simple - Amazon's help page tells you how to do this. And you might find the tips below useful.
Which Amazon site to use?
Amazon expects you and your spouse/parent to have logins in the same Amazon site e.g. amazon.in. Needless to say, use the same site to perform this operation too. (Otherwise, you will not be able to add the other login as part of your family - the error message does not exactly say so, but I found that's the case).
Settings for sharing content
Do this either on the Amazon site or on the Kindle device you own (e-reader or Fire HD tablet). I did it on the site and not on a device - if you have a device and find something of note, please add a comment.
Along with content, Payment methods must also be shared with your spouse/parent.
Accidental purchase
If you are sharing content with an aged parent and would like to prevent accidental purchases, there is no one particular setting that helps, but the following can.
Physical items
Turn off the 1-click setting so that the payment page appears which would tell your parent that they hit Buy by mistake. Even if the process went all the way and the order has been placed, it can be cancelled till items are actually shipped.
Other items like e-books, apps, games etc.
Orders for other items, for e.g. e-books, apps and games, can be cancelled within 30 mts of placing the order for a full refund.
Kindle reader app for Windows 8.1 (specific case)
When you click on the shopping cart icon in Kindle reader, it launches a tab in the browser and takes you to the Amazon page. Which means, to prevent accidental purchases, you can log out of the Amazon site in the browser. This does not affect the functioning of the Kindle reader.
