Madrid to Grenada
 

What would be the best transportation from Madrid to Grenada?

You'll need an aeroplane, unless you mean Granada.
I got the following from Ryanair's website:
The train staion of Granada is fairly central and is in Avenida de Andaluces off Avenida de la constitución. The phone number is 958 27 12 72. Granada is not on a high speed line.
The Talgo takes about 5 and a half hours from Madrid.
[But the Talgo is a high speed train - I just checked Renfe's site and there is an Altaria train that takes 4½ hours twice a day.]

More from Ryanair:
There are many buses each day to and from the large Spanish cities. The main bus company in Andalucía is Alsina Graells. You cannot buy tickets online from their webpage. To do so visit alsa.es. You can check times and prices and even choose your seats. The Granada bus station is slightly out of town and you will need to get a taxi to get to the centre.

From Madrid
If you are coming from Madrid you will need to go to "Estación del Sur".

The nearest tube station to "Estación del Sur" is Méndez Alvaro. The buses go about every hour and if there is a busy day, for example before or after a fiesta they put on more buses according to demand. The usual thing is just to go to the bus station and get on the next available bus. You would be unlucky if you have to wait longer than 2 hours for a bus. Try the Enatcar window. It takes about 5 hours from Madrid to Granada and costs around 16 euros.

frugaltraveler,
Iberia has some round trip fares Madrid-Granada this summer for $95. The Granada airport is officially called the Federico García Lorca Granada-Jaén airport.

For such a short journey, it hardly seems worth the hassle (to me) of queueing in an airport, and paying so much money. You'd see a lot more scenery by train - even more by bus.

I took the trip via bus and it took 4-5 hours, i believe... but I definitely preferred that over the hassle that i had with Ryanair in another trip... the bus is fairly inexpensive, and i enjoyed seeing the country and everything. i wouldn't fly, if i were you..

no, on second thought, my bus took more than six hours. Sorry about that.. it's been awhile since i've been.

Ryanair are quoted as saying "The Granada bus station is slightly out of town and you will need to get a taxi to get to the centre."
There is no need to get a taxi. Frequent buses go from the bus station to the city centre. The fare when I was there last December was 1.10 euros.