How do you say "social network" in Spanish?

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red sociál

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Red social

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Just like Maho and Mathias have just told you "social networks" are "redes sociales" 
because "red" can be like "rojo" if you mean red colour, or it can be "network" 
On the other hand "social" means the same "social" 
For example: 
1. La araña está creando una gran red - The spider is creating a big network. 
2. My brother is a network administrator - mi hermano es administrador de las redes. 
Examples for "social"
1. Her social life is great - Su vida social es genial. 
2. She is very social person - Ella es una persona muy social.

I hope it was useful. If you have any further questions, feel free to ask me.
If you need classes, you can book them here: http://www.italki.com/teachers/professional 
have a nice day.

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Mis amigos espanolas la llaman simplemente ''La Red''

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Se llama "red social": https://es.wikipedia.org/wiki/Red_social