Another airplane almost hit me, but an ACAS Resolution Advisory told me to climb first. Now what?
Well, #2 is actually surprisingly easy. At the top middle of the NTSB website, under "Other ways to Contact NTSB" there is an innocuous-looking link that says "Submit a TCAS Notification" (which has you send an email to tcas@ntsb.gov).  Personally I'd follow that up with a phone call to the appropriate regional NTSB office as well, just to be sure you've discharged your obligation under NTSB 830.  

The minimum required information for NTSB reporting is described in 49CFR830.6: 


  
  Type, nationality, and registration marks of the aircraft;
  Name of owner, and operator of the aircraft;
  Name of the pilot-in-command;
  Date and time of the accident;
  Last point of departure and point of intended landing of the aircraft;
  Position of the aircraft with reference to some easily defined geographical point;
  Number of persons aboard, number killed, and number seriously injured;
  Nature of the accident, the weather and the extent of damage to the aircraft, so far as is known; and
  A description of any explosives, radioactive materials, or other dangerous articles carried. 
  


There is also a FAA website (www.tcasreports.com) which pilots are encouraged to use for reporting TCAS events - this site is not connected with the NTSB, and would not seem to cover that reporting requirement, but including the information that site asks for in your report to the NTSB would probably be helpful as well.



For #1 things seem a bit murkier: I too could not locate anything from the NTSB or in FAA AC 120-55C that clearly defines "necessary to avert a substantial risk of collision", but broadly I would imagine any Resolution Advisory (RA) is reportable, while Traffic Advisories (TA) would not be.
(The reportability of RAs would seem to be doubly true if you're operating in IMC, where you have no chance of visually assessing the hazard -- Complying with an RA there would seem essential to me.)



Note that AC 120-55C does allow a pilot to disregard a TCAS RA if they're certain that they have visual contact with the aircraft causing the RA - but it also cautions that it's difficult to be that certain:  


  Unless it is unequivocally clear that the target acquired visually is the one generating the RA and there are no complicating circumstances, the pilot’s instinctive reaction should always be to respond to RAs in the direction and to the degree displayed.


Presumably in a case where you're operating in VMC, it's "unequivocally clear" that you're looking at the aircraft responsible for the RA, and it's "unequivocally clear" that the traffic does not pose a substantial risk of a collision then following the RA is not "necessary to avoid a substantial risk of a collision" (i.e. you wouldn't have to report the incident).
I'd err on the side of reporting those events anyway though: If nothing else it serves to make the NTSB aware that something happened, and if they see a particularly large number of "somethings" in a given area they may take that up with the FAA to try to isolate and address possible underlying causes...