Would this be a good idea?

I was thinking about contacting some local SEO company's in my area and asking if they would let me shadow/intern there. I'm not in school for SEO and I would of course word it better. Does anybody think any local company would let someone like me do that?

Probably, and it never hurts to try. If they all say no, all you've lost is a little time.

eimFlood said:

Probably, and it never hurts to try. If they all say no, all you've lost is a little time.

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What do you think would be the best way to contact them? Should I just send an email out to all of them or should I just call and ask?

See if they have any openings on their site. You can also try to contact them via linkedin.

I would also start working on some personal SEO projects as well. It's always great to demonstrate some success.

As thedomainkings said, linkedin is a good path.

Even if they don't have openings on their site, you can probably find a jobs@ address or something similar. I'd try that and then follow-up with a call a few days after the email if you don't get a response.

Personally I would give them a call asking for work experience, pass on a covering letter and CV as if you were applying for a job. They should be more than happy for a spare pair of hands working for no cost whilst providing you with a little training.

Go ahead and call them, you will look more professionally if you call them than e-mailing them. If i owed a SEO Company, i would be more than glad to hear that someone is interested to work for me (i actually owed a small business/brand for web services and i was always glad to hear people that were interested to work with me)

Both approaches - call and email - have their pros and cons.

But bear in mind - no company hires anyone to teach them and letting them being payed while being taught. You should express your willingness and readiness for work not with words, but with actions and experience. Show the employer what you did your self do get ready for job, make an impressions of moving the learning path already.
In the regard email may really be a better option. You are given enough space to write down info about yourself and the employer will have time to review it.
In your case, the call conversation, especially with no professional or semi-professional background, will not last long.