1. I know that Reykjavik is the most useful destination in Iceland. If you're exploring Iceland, this is where you start. There is an up and coming airline that operates out of Reykavik, WOW Air. They have super cheap promotional flights from some major international airports in the United States. Indianapolis is not one of them. Their cheapest flights come out of Boston, Baltimore, New York and Miami. A quick search of their website tells me that the best flights in early June will be coming out of Boston. There are a ton of dates you can get round trip for $250.
2. So now we just have to get from Indy to Boston on the right dates. So I open a new browser window and go to Skyscanner. This is an invaluable resource when it comes to travel planning. This isn't the end-all be-all of cheap fares. Just as with Priceline and Hotwire, this website doesn't include all airlines. Their fares also aren't completely up to date. Their data updates as people complete searches, not as fare prices change. While it isn't perfect, I find it is the best place to start when investigating for low fares between two airports. They have a month fare calendar option and you can also easily adjust the scheduled flight times which is very important when booking two separate tickets instead of a flight with a connection on one ticket. The mobile version of Skyscanner is lacking some good tools, so check it out on desktop for the best experience.
3. By searching the dates, I see that Delta offers a nonstop flight from Indianapolis to Boston for just over $100. Checking the fare calendar confirms that I can't save any money by leaving or returning a few days differently. I also check Cincinnati to Boston just to be sure I'm not missing a deal. I can book both flights, to Boston and back to Indy, through Delta for $221.
4. At this point it is very important to check your flight times. You are creating your own layover by booking two separate tickets. The rule I go by is at least a three hour layover for domestic travel and four to five hours for any international flight. You might even book a longer layover for the peace of mind. Sometimes it even makes sense to book your second ticket for the next day and take the night to explore your layover city. If you're traveling internationally or you've checked any bags, you'll have to leave the terminal and go back through security at the second airport. Delays happen, and if for some reason a problem with your first flight causes you to miss your second flight, the airlines are not obligated to help you out as they would be when you book the single ticket. Another way to minimize this risk is book all four legs of your journey, the there and the back, as four separate one way tickets. When you've booked a round trip flight and for some reason you miss the first flight on the ticket, they will automatically cancel the return portion of your ticket. This is no bueno. By booking four one way tickets, you are ensuring that if something does go amiss with one of your flights, your remaining flights will still remain intact.
5. Leave your luggage at home. I'm a firm believer in traveling with carry on luggage only. I usually only pack a backpack. This is considered a personal item and it's free to travel with, though some airlines do have size and weight restrictions. I find it very easy to live out of a backpack for a week. It really is do-able, I promise. I will sometimes pack a carry on IF it's free. By not checking any bags, you save the cost of paying for the bag, which can be up to $50. You also eliminate the risk that your bag will be lost and the need to wait for it at baggage claim and possibly save the hassle of going through security a second time.
And that's how to get to Iceland from Indy for a week in June for only $461. It's true there's a little risk involved, but you're saving $324 per passenger. That means if you're traveling as a couple you're saving $684 which would cover your accommodations for the week, and to me that's worth the risk. Yolo, ya know.