Let's assume your folder structure looks like this:
/css /images /js index.php
Copy dsg.php into your main directory:
/css /images /js dsg.php index.php
Now, create a default gallery folder called ds_galleries (if you wish to change it to a different name, see custom script location):
/ds_galleries /css /images /js dsg.php index.php
On some servers you may also be required to change ds_galleries folder permissions.
Permissions can be changed through shell access or a FTP program like Transmit (OS X) or FileZilla (OS X, Linux, Windows). In Transmit just select the folder and hit cmd + i, in FileZilla right click on a file and choose "File permissions". Their settings windows look similar so I'm going to focus only on Transmit.
Standard settings on my server were 755, which allowed the script to work out of the box. Depending on your server you might be required to set permissions to 666 or even 767 (optionally 777 - but that's a dangerous one). The important thing is for user to have the ability to write to that folder.
For more info about changing file permissions I recommend asking Google or consulting your hosting provider.