There is nothing like packing everything you have in a backpack and lugging up and down mountains all day in god only knows what kind of weather, only to do it all over again for the next 150 days. So how do you even begin to get ready for that? I'm not sure, but here's what I've been trying.
Hike as much as possible! Seems obvious. Luckily I live in an area with a nice state park with what people might consider "mountains". They may not be huge, but they don't have to be. Every time I go out there I feel like I could go a little farther and a little faster, even though I try to carry more and more weight each time. After about the tenth time I hiked the entire state park, I didn't even get paralyzingly sore the next day! Just really, really sore. Improvement!
Practice with your AT gear! I still need lots of practice, but I feel like I could at least survive out there now. It doesn't seem like it would be so hard to figure out how to set up your tent, cook food, filter water, or pack your pack, and it's not. There are certain tricks and layouts and timing that you only figure out by practicing the seemingly simple chores over and over though. You could figure all of it out in a week on the trail, but that could lead to a hellish first week of extra time in the cold because it takes extra long to collect your water and set up your tent. And that hot meal you were looking forward to turned out to be way to watery and cold because cooking on an alcohol stove isn't the easiest thing. Just get the rookie mistakes out of the way at home. Many people quit in the first week and not knowing your gear won't help you avoid that fate.
Read and study and get advice from reputable sources to know what lies ahead of you! Most people quit their thru hike because they are not mentally prepared. It's like Yogi Berra once said, "Baseball is 90% mental -- the other half is physical." Same for the AT. Read previous thru hikers blogs or books. Better yet talk to a thru hiker if you know one or email a thru hiker who is an active member of the hiking community to get personal accounts of what it will be like. There are references everywhere out there. Look at everything, watch everything, read everything, and talk to anyone you can. Know that there will be bad days, but also know that there will be indescribably awesome days. And I don't just mean awesome dude, I mean days just full of awe.