From 0.97.[x] to 0.98

The current version features an installer that takes care of upgrading all elements if previous version are found.

Do not put your data at risk: do a site and database backup before attempting any upgrade.

From 0.96.[x] to 0.97

Backup
Download the upgrade package
Unzip
Upload to target website
Run this query *:

ALTER TABLE jos_custom_properties_fields ADD modules varchar(255) AFTER field_type

*To run  the query you need either access to mysql command line client or to a web applications such as phpmyadmin.
The query assumes that the table prefix is jos. Make sure that the query matches the table prefix of your Joomla installation.

Note: if you are upgrading from version 0.95, you first need to upgrade to 0.96.

Revise your CSS, because id=search, id=searchform, id=text_search have been replaced by "class".

From 0.96 to 0.96.1

Backup
Download the upgrade package
Unzip
Upload to target website

From 0.95 to 0.96

alter table jos_custom_properties add UNIQUE KEY `c_f_v_id` (`content_id`, `field_id`, `value_id`)