There are direct flights to Scottish airports from England, Wales, Ireland, the USA, Canada, Scandinavia and several countries in Western, Central and Eastern Europe. From elsewhere, you'll probably have to fly into a European hub and catch a connecting flight to a Scottish airport – London, Amsterdam, Frankfurt and Paris have the best connections. This will often be a cheaper option anyway if flying in from North America.
Scotland has four main international airports: Aberdeen, Edinburgh, Glasgow and Glasgow Prestwick, with a few short-haul international flights landing at Inverness. London is the main UK gateway for long-haul flights. Sumburgh on Shetland has summer service from Norway.