You probably will not be able to use a 'free' webhosting service, because Opensis-ce requires MySQL. You should call or e-mail webs.com and see if they think your application can be moved into their site. I think they may have a bundled solution that doesn't make account of installing your own database driven apps. An e-mail or call to sales should clarify that.
Opensis-ce list their minimum requirements as Apache 2.2, PHP, MySQL 5.0, so you need a hosting company that has those services.
You should really ask over at: http://os4ed.com/forum/index.php
Unfortunately - they don't seem very committed to answering questions.
The short answer is:
A. You need a webhost that has the minimum requirements -> Apache 2.2, PHP, MySQL 5.0
B. You will need to export your database using a tool like phpmyadmin. The output file from that will need to be imported into the database on the webhost.
C. You may need to run an installation process to get your php files installed, or you may be able to copy them, there's no way for me to guess.
It looks like they offer their own hosting service, so that may be an option also.
There's really no way for us to know the 'right' answers because we didn't make the software. You should contact the developers, Opensis.
If you can't find a free webhost, there are lots of very low cost ones that meet the requirements. We are talking perhaps $4-5/month.