Put in a new HVAC system and upgraded all my insulation in October 2016. I did not claim this on my taxes last year. Can I claim this year? How do I know I qualify?

No, you would have to report it on your 2016 return.

Insulation (part of a system designed to prevent heat gain, heat loss, or air infiltration) is eligible for a 10% credit on cost of materials only, not including installation.

An efficient air conditioner is eligible for a 10% credit on the cost of materials plus installation ($300 max) if the unit meets the highest efficiency tier that has been established by the CEE as in effect on January 1, 2009.  You would have to check the manufacturer to see if the A/C is in the highest efficiency tier.  

Also, the maximum credit for the A/C is $300 and there is a $500 lifetime maximum for all residential energy efficiency credits (going back to the start of the credit in 2005).