How do I nicely tell my neighbor (That I currently have no issues with and don't want to really start any) that if she doesn't #1 start putting her dogs in at night, or #2 get them some serious training so I'm not woken up by them multiple times throughout the night and have to hear them all day barking at nothing, I'm going to call animal control until something is done?!?!
You can't honestly tell me she doesn't hear them! And how does it not bother her?!? 

You just nicely do, some people can not stand to even be told nicely something. So as long as you go over there and are nice about it, than you did all you can do without calling someone. I don't know how people can stand listening to dogs bark, we teach our kids manners, I taught my dog manners. If he barks I say the word leave it and he stops barking. 

I don't know how to even start the conversation though. We only say "hi" in passing and have never had a real conversation so I dont know if I should just walk over and knock on her door or wait until we run into eachother again and just be like "oh by the way." 

Ya, that I can not help on, I do not like to tell people what to do even if it is bothering me. I am to nice, but you can only take so much. My neighbors dog howls, one day I tried to comfort him so I didn't have to hear him, I asked her one day what his name was so I can comfort him when he howls, it was a nice way to start it. She said sorry and realized I notice and it bothers me. It worked out well 

"Hey, I don't know if you realized, but your dog barks all night long (or whatever else the specific description is). I've heard that one of the neighbors is talking about reporting you so I thought I'd warn you before they do. Have you considered crate training or hiring a trainer?"

Or leave a note. 

Just call animal control. They can leave a copy of whatever nuisance regulations your area has with her. 

Why does no one keep their dogs inside at night time?

At cherry point dogs wern't allowed outside at all unattended even if they were in a fence. 

^ I thought that was the rules here too but I don't live on base so I'm not sure. If it is the rule, it's not enforced at all. 

I would leave a note. And, give them a few days if nothing changes call animal control. 

I would leave a note, too. Just as sweetly as you possibly could. That would be the first step. 

I would call for sure. How can they stand to listen to that all night? That is SO irritating. Plus, they may just revert back to their old ways and leave the dog out again, and then you'll have to call anyways.

Odds are they are just jerks if they leave their dog outside all night! Who does that? But then again, I am one of THOSE people who sleeps with their animals...