1. If you have any type of breakdown cover then use it, if you have home start cover then call them out. They will do a diagnostic check. Giving you the codes. Then either call up FIAT or google it.
I first had this problem, got GreenFlag to come out and do diagnostic check. Came back as coil issue. Noticed there was a crack in the coil pack so replaced both coil pack and HT leads. fixed the problem for 2 years. But then started doing it again. This time I pulled the leads one by one to check that there was a spark. No problems with leads or spark plugs. Although noticed that when pulled lead 3 out the car would still idle and not cut out. So thought would be failed coil pack again, replaced it for an OEM £15 inc P&P off ebay. fitted it but still had the idle and power issue although it had improved slightly.
Will need to call out GreenFlag again but i doubt they will find the issue as it's going to take alot more investigation and probably trial and error part replacing to find the fault. I saw also that other Punto owners replaced ECU's, Lambda sensors, even a blocked exhaust, fuel pump & lines to get their "common" idle/power issues fixed.
I will not go down that route. I will simply flog the car off and have to buy another 2nd hand car that is less prone to these issues as is the case with Fiats.