Motorcycle Repair: 81 Honda CX500 wont fire, CX500, HTTA

Question
Just bought this bike, it turned over fine upon inspection, and upon reaching home.  Today it will turn over, but not fire.  Charged battery to ensure this was not an issue.  What might be the most likely cause and resolution to try first.  Thanks.  (New to motorcycle engines, but know enough to try basic repairs)

Answer
OK, I'll assume that you know that the kill switch (on the right hand switch cluster) needs to be switched to "RUN" and the petcock (under the left hand side of the fuel tank near the back) has to be switched to "ON" (or to "RES" if the fuel level is low).
Don't ask me why these possibilities come to my mind so quickly ;-)

If it started & ran within the last week or so and the fuel & kill switch are turned on the problem is probably something fairly minor - a sparkplug cap that has been pulled off and not pushed all the way back on or a  sparkplug wire that has been pulled out of the sparkplug cap for example.

If it sat longer between times there are other things that can go wrong - fuel that evaporates in the carbs can leave a coating of varnish that can keep the float valves from opening or block a jet.

There are too many possibilities to cover them all in one reply here.

My recommendation is to try the simple things first (such as I have mentioned above). If that doesn't help it will at least eliminate them from the list.

I would like to invite you to join the Honda Transverse Twins of America (HTTA), an online club for people with Honda's original series of V-twin engines - the CX/GL500/650 family.It's absolutely free to join and there are no dues or anything like that. http://choppercharles.com/cs/forums/  
On the HTTA forum you will find a lot of people who have bikes like ours and there is likely to be someone who has already done what you need or want to do and is more than willing to share their experience & insights with you.
BTW: I am a long time HTTA member. My current sidecar machine is based on an '84 CX650 and I previously had an '82 GL500.

I look forward to meeting you there, whether the easy suggestions above help or not. If they don't solve your problem, ask on the forum and a bunch of uswill jump in and try to help.