As to the land transport - there is a rather good concrete-plates road (partly metalled road) from Usinsk town directly to Kharyaga oil field. The deposit itslef is situated on the federal road Naryan-Mar - Usinsk (which is 90% finished). There are daily buses (only for shuttle workers) to take people to Usinsk from the deposit. So if you a stranger at Kharyaga the best way to get away from here - auto-stop (just stop the passing car and ask for favor). The way from Kharyaga to Usinsk takes 3-4 hours (depending on car's speed and weather conditions). From Usinsk you can rent a taxi, but I guess the price will be rather high, because they will have to charge the double tariff.
Because of oil production and lack of roads the most popular way to get to Kharyaga from Naryan-Mar is a helicopter. They have 2 landing areas here, one is just next to the settlement and the other at so called Kolvinskaya. At Kolvinskaya they also have a controller's tower and filling-up for helicopters. The air traffic here is really heavy. Sometimes helicopters land and take off every 30 minutes. They bring shuttle-workers and cargos to and back. The way from Naryan-Mar to Kharyaga or back usually takes 1 hour, but the helicopters often land on the way near different points (like oil-rigs).