I have a 2014 Fiat Punto and have been using 92 octane gas. I have never read the manual, but am now told I should use 95. Should I use what is in the tank before filling with 95 or is it OK to mix them.
It's not a problem mixing them. Just start using 95 if that is what the engine calls for. You'll not create any issues doing so.
Modern day engines have sensors which can adjust for the fuel. If yours calls for 95, but you're running 92, the engine most likely won't be putting out the power it would on the 95. You probably won't notice a difference in driving, but you might. Anyway, its nothing really to worry about mixing the two.
Presumably since you say "92 octane gas" you are not in Europe.
The whole topic is a mess, because there are different scales for measuring "octane". The most common scale world-wide is RON, but there is a different scale known as MON which produces lower numbers, and in some countries (particularly the USA, Canada, and Brazil) the numbers on the pump are actually the average between RON and MON. The MON number can be as much as 8 points lower than the RON for some fuels.
The Punto was designed in Europe, and none of this is an issue there, because grade are always described in RON and the cheapest "regular" gasoline grade available almost everywhere is 95. If lower RON grades are on sale they are sometimes more expensive than 95 because of the small demand for them. For example a typical UK gas station sells "premium" 95 ROM ("premium" being marketing-speak for "lowest grade", of course) and "super" 97, and possibly a higher grade (e.g. 99, 100, or 102) with a brand name from a particular oil company (Shell, BP, etc).
A modern car (say, post-1995) will run on lower octane gasoline with reduced performance (power, economy) and no other issues.
Older cars did a lot of nasty things ranging from occasional "pinging" or "ringing" noise and accellerated engine wear to complete engine failure.
Then again, one cannot easily find these days neither a pre-1995 car nor a gasoline with low enough octane number in order to create problems in a car built for pre-1995 standards gasoline.
p.s. it is OK and pretty much advisable to mix some '95 gasoline into '92 in your tank