Quite confusing with "Haircut"
How do you say "I had my hair cut yesterday."?
3 Answers
How do you say "I had my hair cut yesterday."?
One option:
Me corté el pelo ayer. Literally it means I cut my hair yesterday.
Reference on why it works (this example is present tense and then future):
http://www.spanishdict.com/answers/7112/cortarse-el-pelo
Lazarus:
There is a way of saying "I get my hair cut" in Spanish, but it results in a rather long sentence compared to the English version, or with "Me corto el pelo", so people resort to this version.
The "se" in "cortarse" has several possible meaning. Now, the majority of people don't normally get a pair of scissors and just cut their hair, but pay for someone else to do it. When people say "Me voy a cortar el pelo", cultural common sense dictates whether the person is really going to cut his hair (not again!) and make a mess, or going to a professional, and get his hair cut. In most cases, it means "I am going to get my hair cut", and you'll hardly ever hear the more rational (but longer) "Voy a que me corten el pelo".
I am a learner, await other thoughts.

I had my hair cut translates idiomatically to me corté el pelo.
The nuances are different.
In English, have something done means that you arranged something for someone to do it, that is: you didn't do it.
In Spanish, this construction doesn't exist because we simply say me corté el pelo or me cortaron el pelo. Those two are active sentences and we'd be literally saying tuve mi pelo cortado, which is utterly unidiomatic.
Remember that expressions need to be understood as idiomatic as possible. The idea is to learn how to use the language and not to translate it, because that's what translators do.
"Voy a que me corten el pelo"
In Mexico this is exactly how I have always said it and anyone who I know as well, but I left there in 2001 so maybe there is a different usage now. As Lazaruz said, this is the most rational but longer way, but this also the correct way grammatically. Also I have found that if certain people don´t have the time to listen to you speak because you may use more words than others, then they are not worth your time. So don´t rush on their account.