Most common and viable way to reach Iceland is by air, by ferry is also an option, however, most people prefer flights.
Keflavik airport near Keflavik is the largest and most central international airport in Iceland - it is quite desolate and barren (about 40 km from Reykjavik) so long layovers might get boring; For domestic travelling and flights to Greenland and the Faroe Islands, Reykjavik airport is the go-to point. Icelandair is the best airline (low-cost and frequent) to Iceland from major states in USA and Canada; WOW Air - flies to Iceland from 14 major European destinations; known for low fares and the in-flight experience. (However, it's always advisable to clarify details like luggage limit and charges before booking) Travellers are advised to watch out for offers and promotions as otherwise travelling to Iceland might be expensive.
Smyril Line is a ferry that sails weekly from Hirtshals in Denmark to Seyðisfjörður in Iceland via the Faroe Island, taking 2 nights to complete the journey.