When you visit this forum on your Android phone, you should be automatically be getting a message asking you to download Tapatalk. Go ahead and download the Tapatalk app here:
If you visit the above link with Google Chrome, then it will let you remotely install it on your phone. If you want to do it manually, then go to the "Play Store" app on your phone and search for Tapatalk.
As for the forum working well on a mobile phone WITHOUT an outside program like Tapatalk... not with the current version it won't. This forum is running vBulletin 3.7.x which is rather antiquated. Unfortunately vBulletin 4 is already at a development standstill (and costs $250) and vBulletin 5 is an absolute trainwreck. Most forums that have switched to vB5 have died a horrible death as people quit due to all the bugs and sluggishness and missing features.
The amazing developers who created vB2/3/4 left the company to form their own forum software company -- XenForo. It's streamlined, simple, and works great on mobile phones. Upgrading this site to XenForo is the most logical next step, if the site owners decide to invest some time that is. I hereby volunteer my time as I've got 12 years forum administration experience.