Hello johnr9q, to race the national games you have to qualify during your state's senior games during the PRIOR year. So to race in this year's (2013) games you had to compete in your state's 2012 games and be in the top 2 or 3 (varies by state).
From my experience, jumping into races at the state level is OK if you have some significant group riding experience. If not, find a local club and learn the etiquette and techniques of group riding. You can find some road racing and time trial advice in the "33" racing sub forum in the stickies but you can only really learn by doing.
If you are interested in competing in the national games, compete in your state games this year and then try to qualify next year. Also, if you live anywhere near Utah, you can try competing at the Huntsman World Senior Games. They have races for seniors with different levels of experience; from first-time racers to very experienced racers.
Hope this helps.