Madrid Train or Metro from Airport

Taxi. Metro requires change

I agree with Frank.

Cercanias train also involves one change & you will be carrying your luggage.
Keep in mind that you may be exhausted from lack of sleep & jet lag too.

Edit: It's Puerta del Sol not Puerto del Sol

Thanks for the taxi recommendation but my Husband prefers either Metro or Train. I would like to know where you would transfer between Terminal 4 and the SOL station?

There is also a van service, Aero City. It can be booked in advance, as well.

Pam,
You would take the Cercanías train ( commuter train) C-1 line ( light blue on the map here) from Terminal 4 to Chamartin Station ( or to the next stop, Nuevos Ministerios), then transfer to either
C-3 ( purple) or C-4 (navy blue) to Sol.

You may check Cercanias train schedules here: http://www.renfe.com/EN/viajeros/cercanias/madrid/

Wishing you a wonderful trip!

I know you said your husband prefers train or metro, but just in case one or both of you change your mind when you actually arrive (I've done that many times), know that a taxi has a fixed rate of €30 and no tipping is required beyond this.

Using the Metro is very easy, especially if you have ever used any Metro before. This spring I used it to go from the airport to Gran Via....two changes. Go to Metro website, write your connections on a card and try it.

Pam,
Keep in mind that taking the Cercanias train (as explained above) will involve one transfer vs taking the Metro which will involve 2 changes.

Here's Madrid's Metro website.

Have you decided which form of transportation you will be taking?