How to find cheap fares and options

[NomoneyNohoney]

Delightfully simple: For most people, Google Flights is the simplest, most user-friendly option for finding cheap fares. The Google Flights fare calendar makes it easy to search low fares and their fare map allows users to enter a departure city and search for the cheapest destinations around the world. Google Flights will even notify users if changing their travel dates will save them money.

https://www.google.com/flights

Read more at: Five Expert Tips for Finding Cheap Fares | Frugal Travel Guy

[Lootman]

Delightfully simple: For most people, Google Flights is the simplest, most user-friendly option for finding cheap fares. The Google Flights fare calendar makes it easy to search low fares and their fare map allows users to enter a departure city and search for the cheapest destinations around the world. Google Flights will even notify users if changing their travel dates will save them money.

https://www.google.com/flights

Read more at: Five Expert Tips for Finding Cheap Fares | Frugal Travel Guy

Yes, seconded, I've been using it for about a year now, and it's the best fare finder that you don't have to pay a fee for.

It's also great how you can broaden a search, say, by selecting London (multiple airports) and having your destination as an entire country, e.g. Japan. And, as you say, it will suggest different dates or alternate airports if there is a saving.

It also allows for very easy searching for specific airline alliances, number of stops or by class of travel, which I find useful, as I am often willing to pay more for such flights.

[NomoneyNohoney]

Thanks. I have been looking for flight prices Seoul (any airport of the two there) to Jeju Island and return. Skyscanner returns flights from GBP 151 return. Google Flights returns flights from GBP 254 for the same dates.

Neither of those options gives prices for the several no frills carriers who do this (extremely busy) route. I know you can get flights from about GBP 15 upwards each way if you book well ahead, but I can't seem to find a search engine that returns those flights.

Any ideas what can be done, or s it not possible to show no frills carriers in searches? (Perhaps I need to ask a Korean friend to look for me!)

I use a free, wonderful iphone app called Rome2Rio.
Using your locations, I get the following suggestion;
Seoul - 19min by train £4
Seoul Gimpo (GMP) 1 hr 5 mins by plane £24 (The app shows timetables for 5 airlines*)
Cheju (CJU) -48 mins by bus, every 30 mins £4
Hotel Shilla - 31 mins by foot 2.6 km
Jeju Island Pension

*Trying to identify the airlines, GMP-CJU, I think they are:
Jeju Air jejuair.net (sale on at the moment!)
Air Busan flyairbusan.com
Korean koreanair.com
Jin Air jinair.com
Asiana Airlines flyasiana.com

HTH