Airlines do sometimes publish fares that are different based on the “Point of Sale” (POS), which basically refers to the country in which the ticket is purchased.
As an example of why they do this, consider flights between the US and Australia in July. July is summer in the northern hemisphere but winter in the southern hemisphere, so there is likely to be more demand from Australians visiting the US at that time of year than there is people from the US visiting Australia. As a result of this demand, the airline may choose to increase the price of flights for Australians (who are more likely to pay them as they are headed to summer!) and keep the price the same for Americans who would not be willing to pay the higher charges.
So yes, this does happen. Not always, but sometimes.
So the next question is how can you make use of this? The simple answer is that it depends on the airlines involved.
Sometimes simply using a travel agency in the country you want to book from is enough. That could be a physical travel agency (eg, via phone/email), or an online travel agency. Sometimes you can use the local website of the airline that you’re wanting to book, or even just their global website but changing the country selection on the website (eg, United Airlines has a dropdown box on their website to select the country).
In general there’s no need to be seen to be in the country that you’re booking from, so generally no need to use a VPN – although it’s certainly possible there are websites out there that do require this.
However as you can imagine, airlines generally don’t like you doing this as it costs them money! As a result, over the past few years they have started taking action to stop this from happening. Travel agents that repeatedly exploit this loophole have received warnings to stop doing it (and can potentially be “fined” by the airline on the basis that it is normally against their agreement with the airline to make such bookings).
Many online travel agents and some airline have added additional checks to stop people abusing this loophole. For example, when booking a ticket on the United Airlines website, if the country your credit card is from is different to the country you’re claiming to be from, then it will re-price the ticket using your credit cards country. Unless you have credit cards from multiple countries, then it’s not possible to book these flights via their website!
Also if your credit card has foreign transaction fees, you will need to factor these into the price – you’re going to be charged in the foreign currency so you’ll be hit with a conversion fee (often 3% or so) unless you have a payment method that doesn’t charge such fees.
As far as finding such “deals”, the ITA Software “Matrix” tool will allow you to set the “Sales City” which will act as the point of sale (You can also set the currency, which will affect only the displayed price and NOT the point of sale).
For example, using that tool for a flight from Australia to the US in July as mentioned above, the flights between SYD-SFO-SYD for some random dates costs US$1,976 if purchased in “Sydney”, but only US$1,738 if purchased in “San Francisco” – so in this case someone from Australia could save US$250 booking on the US site rather than the Australian site (presuming, of course, they could find someone in the US that would actually sell them the ticket – the United.com website would not!)