-UPDATE- Openmeetings version 2.0 is out, and was a lot easier to get up and running via the supplied Binaries.
(You could still download the source and use the rest of this article as a guide)
Get the Binaries Here

Openmeetings provides video conferencing, instant messaging, white board, collaborative document editing and other groupware tools using API functions of the Red5 Streaming Server for Remoting and Streaming.

Getting it up and running to a 'useable' state was no small task. (Well, at least for me it seemed pretty daunting) So I'm posting the steps I used to get it off the ground.

RHEL 6

Repos

rpm -Uhv http://apt.sw.be/redhat/el6/en/x86_64/rpmforge/RPMS//rpmforge-release-0.5.2-2.el6.rf.x86_64.rpm

Getting the Source (Make sure you start in a good directory. I made ~/Software for this purpose)

svn checkout https://svn.apache.org/repos/asf/incubator/openmeetings/trunk/singlewebapp/

Dependencies (Yum)

yum install ant ant-junit ant-trax ghostscript sox mysql-server

Dependencies (Java)

You will need to download Sun Java JRE and JDK and install them. I chose the '*rpm.bin' files since all you have to do is execute them to install. JDK JRE

chmod +x jre-6u33-linux-x64-rpm.bin
chmod +x jdk-6u33-linux-x64-rpm.bin
./jre-6u33-linux-x64-rpm.bin
./jdk-6u33-linux-x64-rpm.bin

Test Building the Application (Assuming you are still in the ~/Software directory)

cd singlewebapp
ant test

This is where I had the most headaches. Most, if not all, of the dependencies should be accounted for at this point, but if you don't get a 'build successful' (or the like) you need to do some digging.

Assuming, everything went well, build the application with the following command

ant

You should now have a directory structure similar to this.

drwxr-xr-x  7 user group   4096 Jul 20 13:10 build
-rw-r--r--  1 user group    442 Jul 20 10:58 build-jaudiotagger.xsl
-rw-r--r--  1 user group    154 Jul 20 10:58 build.properties
-rw-r--r--  1 user group  43100 Jul 20 10:58 build.xml
-rw-r--r--  1 user group  19803 Jul 20 10:58 CHANGELOG
-rw-r--r--  1 user group    706 Jul 20 10:58 DISCLAIMER
drwxr-xr-x  3 user group   4096 Jul 20 13:08 dist
drwxr-xr-x  6 user group   4096 Jul 20 10:58 docs
-rw-r--r--  1 user group   2478 Jul 20 10:58 ivysettings.xml
-rw-r--r--  1 user group   3104 Jul 20 10:58 ivysettings.xsd
-rw-r--r--  1 user group  14892 Jul 20 10:58 ivy.xml
drwxr-xr-x  3 user group   4096 Jul 20 10:58 lib
-rw-r--r--  1 user group 166369 Jul 20 10:58 LICENSE
-rw-r--r--  1 user group    281 Jul 20 10:58 NOTICE
-rw-r--r--  1 user group   4690 Jul 20 10:58 README
drwxr-xr-x  5 user group   4096 Jul 20 10:58 src
drwxr-xr-x  4 user group   4096 Jul 20 10:58 test
drwxr-xr-x 12 user group   4096 Jul 20 10:58 WebContent
drwxr-xr-x  6 user group   4096 Jul 20 11:22 xdocs

To run the software

cd dist/red5/
./red5.sh

And point your web browser at "localhost:5080/openmeetings/install" and make sure to follow the warnings and directions therein.