Using the ITA Matrix

ITA Matrix - not my actual example - but gives an idea of what to do.  

Raffles has written some guidance here and flyertalk has some here.  In addition, although most males are terrible at referring to the 'Help' section, believing that user interfaces should be intuitive, the ITA Help is actually helpful too!

I've found that it's worth fiddling around, doing searches with lots of departure points and few, as often the search results can be different.  In this instance, I have forgotten to specify the route to force ITA to quote for LCY-JFK (as that's 210TP vs 140TP for same price LHR-JFK) by putting in LON BA-14 NYC LAX...but it shows process ok 

self-explanatory; clicking on the highlighted cheapest fare leads to this

it's a very long list, you can expand each entry using a 'details' option on the right of each entyry that is visible when you hover the mouse in that area, but clicking on the fare gives you this

I've no idea whether Alaska First generates any TPs but you get the drift.  The fare breakdown is lengthy and clicking on the fare rule (ILR21AP) gives you a very long fare rule, extract only here but all the sales periods etc are in here