Hi,
I presume you arrive into T1 (if you go with Ryan Air or AerLingus).
There is a 5 min walk to the metro. It costs 2E (standard charge for going to/from the airport).
Then depending which end of Gran Via you are, take :
[1]. Line 8 (pink) to Nuevos Minesterios, change to Line 10 (navy blue) to Plaza de Espana.
[2]. Line 8 (pink) to Nuevos Minesterios, change to Line 10 (navy blue) to Tribunal, change to Line 1 (light blue) to Callao or Gran Via.
You'll need to ask your hotel what metro stop is closer, or look up the hotel address on mappy.com, which will show the nearest metro stops.
It prob wouldnt cost much more than 20E in a taxi, so you mightn't want the bother of dragging bags up and down metro stations.
Maybe Mr Happy can test his orientation skills during the weekend, when you dont have luggage with you!
PS: watch your handbag - there are loads of pickpockets in Madrid.
Ragazza.