For more than one person, the cheapest way to cover the Golden Circle is to rent a car for the day. From Reykjavík, take Route 36 northeast to Þingvellir (watch out for ice in winter), then continue east along the 365 to Laugarvatn, from where routes 37 & 35 run up to Geysir and Gullfoss. On the way back, follow Route 35 southwest to Selfoss, detouring briefly along the way to visit Skálholt and Kerið crater. Selfoss itself is on the Ringroad 30km east of Reykjavík).
Without your own vehicle, you can pack all this into a nine-hour Golden Circle tour offered by Reykjavík Excursions (re.is; 9900kr), Grayline (grayline.is; 9500kr) and Sterna (sterna.is; 9300kr). All can collect from Reykjavík accommodation and a guide provides commentary in English en route.
Slightly cheaper (8900kr return) are Reykjavík Excursions’ daily Þingvellir–Laugarvatn–Geysir–Gullfoss scheduled buses from the BSÍ terminal in Reykjavik, which stop long enough at all the sights for you to get a good look; you can, of course, arrange to spread this trip over several days and stay overnight at places along the way. Be aware too that summer buses heading to Akureyri via Kjölur travel the same route (though most skip Þingvellir), so you might not need to make a separate trip to see the Golden Circle.