As most cities Glasgow has a bus network https://www.firstgroup.com/greater-glasgow, a simple subway with circular lines http://www.spt.co.uk/subway/, trains, and taxis.
Unfortunately, the airports are not well connected and you have to use either bus, train or taxi.
Airports connections are:
- Glasgow International Airport (Airport Express bus https://www.firstgroup.com/greater-glasgow/routes-and-maps/glasgow-airport-express takes you into the city center (Central Station), there you need to take the subway, bus or taxi. A taxi from the airport to the Hostel is about £20-25.
- Edinburgh Airport (ca 1h by bus Citylink Air http://www.citylink.co.uk/citylinkair.php from Edi Airport to Buchanan bus station Glasgow, walk to subway (Buchanan St) or take local bus, taxi to Westend, SYHA Hostel, about 15 min). A taxi from Edi Airport would be too expensive.
- Prestwick Airport (ca 45 min by train https://www.thetrainline.com/ to Glasgow Central station, take taxi, subway to Hillhead St, walk to Hostel). A taxi from Prestwick Airport would be too expensive.