There is no train service directly from Glasgow Airport to center city. You'd need to take the #500 express bus from the airport to Queen Street Station/George Square/Buchanan Street. The bus stops at or near some hotels. Yours may be one of them. You could also take a taxi. Bus costs 8 pounds. Taxi would be about 18 pounds plus tip.
If you're really set on the train, you can take a bus or taxi to the local station in Paisley, then take the train in from there. The local bus service is operated by McGill's (No, not Slippin' Jimmy or Chuck), number 757, which can be found at bus stance 7 at the airport. However, the Paisley (Gilmour Street station) train terminates at Glasgow Central, so you'd need to switch trains at Central in order to get over to Queen Street Station. Or take a taxi.
My choice would be the bus, as it only takes about 20 minutes in to town. Otherwise, it would be bus or taxi to Gilmour Street, train to Central, then another train or taxi to Queen Street. With luggage, that would be too much to deal with after a long flight.