So when you access your web server via FTP, you can see all of the files and folders that make up your site. The 3 main wordpress folders are wp-admin, wp-content, and wp-includes. Within wp-content, you have a folder called "uploads" - this is where your images are stored. They are further organized by year and month (each represented by yet another folder). If you select the uploads folder, you should then be able to access its information, allowing you to change the name of the folder (don't do that tho) and its permissions. It's these permissions I'm talking about. They should be set to 755 (you'll see this number change as you select/deselect the check boxes, looks something like this :
X X X
Verify this setting for the Uploads folder, each year folder, and each month folder. If you see less check boxes than this, then make them all like this. If they're already like this, you can try checking all the boxes (777) and see if that works. It's not the best settings for security reasons, but it will help you narrow down your problem.
To access your site via FTP without going through Dreamhost, there are a bunch of easy to use FTP clients (programs) out there. I use Fetch. Another is FileZilla http://filezilla-project.org/