“Use the customization options”
Each theme serializes and unserializes its options in its own way. Some will pack the options in multi-dimensional arrays others will store as single variable entities.
The state of a theme’s options are stored in the wp_options database. You need to activate the theme and press the Save button to get the data persisted. Start with a clean wordpress install and export the wp_options table to take a snapshot. Then, install the theme you want to look at. Export the wp_options table again and do a comparison.
If the theme does not clean up the options table after being deactivated, you could (if you knew what each option was) conceivably reuse those options stored in the database. However, it would be wise to make a copy and prefix the option with your theme name.
Just bring up phpmyadmin, show 1000 records and then sort on option_name. Usually good themes will store their options with a prefix of their theme name. To see how it serializes and unserializes the data, search throughout the theme code for get_theme_option and update_theme_option to get a better idea of how they store.
Also by “reusing” you need to mimick the forms and the loading, resetting and saving.