Make a test directory /new_shop

Make a test database

Load a backup copy of your Live Site into the test database ...

Load your existing site to /new_shop ...

Load all the files for Zen Cart v1.3.5 ...

Edit the 2 configure.php files:
/includes/configure.php
/admin/includes/configure.php

Change the paths to reflect the /new_shop and the database, username and password to reflect the new database ...

Run the /new_shop/zc_install

Test the upgrade process on /new_shop and you should test everything from:

Create several test account
Add to cart
checkout for your shipping modules
checkout for your payment modules

Complete several test orders ...

Make sure all is happy in My Account and Admin ... Customers ... Orders ...

If all is perfect ... set Live site Down for maintenance ...

Drop all tables from /new_shop database and load fresh copy of Live Site database after it was set Down for Maintenance ...

Run /new_shop/zc_install again ...

Test all again ...

If all is perfect ...

Edit the 2 configure.php files:
/new_shop/includes/configure.php
/new_shop/admin/includes/configure.php

To reflect the Live Shop directory path ...

Do NOT change the database ... you will be now using the new database you made with v1.3.5 ...

Rename the Live Site /old_shop or move to /old_shop directory ...

Rename /new_shop to Live Shop directory or to the root depending on where you have it ...

Check and test everything ...

If all is good ... take new Live shop off of Down for Maintenance ... and you are good to go ...

NOTE: it is a good idea during testing of /new_shop to remove/install Payment, Shipping and Order Total Modules *AFTER* you have written down old settings ... and reinstall and configure ...

Many changes have been made and you want to assure all is right in the world ...