I've got this project that I'd like to become a real thing. I'd say it's about 1/2 in the development process. Important core mechanics are there but it needs more content and stuff like more advanced AI and lots of tweaking. But, visually, I'm pretty confident that it will look no different at the end of the project so people would recognize it even if the gameplay changes a lot.

Let's say the game would be done a year from now, is 1 year too far for people to know of the game? I know of games that weren't shown a month before release and others would have a trailer shown years from release. 

First, how soon should I start sharing media of the game? And how soon should I start marketing to the public?

First, I've learned on estimating things, take your estimate, double it and add 50% and you will be close in most cases to reality.  As the saying goes in game dev/coding, when you're 90% done, you only have 90% left to go.

Now for your actual question, how soon should you start advertising?  Soon, but you have to be willing and ready to keep updates coming and interact with the community you may develop.  It's a lot of work, but if you expect to get much attention a month before release, you will likely be very disappointed from what I've read.

Depends on your marketing plan. If you're going to spend a million dollars on ads to coincide with release, you probably don't need to do any early marketing  
If you're making a multi-player or high-difficulty game, it may be important to begin gathering a community before you launch, so that on release day there's a group of experienced players already.
If you're not sure of your ability to get attention from press, it might be worth trying to start getting media attention one year early, so that by the time you launch, it's possible to google your game and actually find articles written about it.
If you've got something that is honestly innovative, perhaps you want to keep it under wraps until a month from launch to assure that copycats won't appear until afterwards.

It also depends on what kind of marketing you plan on doing. We ran a blog for our indie game for the first 5 years of development and got pretty much zero press (a single mention in one french YouTube channel), so that's pretty much the same as doing nothing. We just exhibited our game at PAX recently though, and have appeared on several gaming blogs, podcasts and youtube channels, and also recruited a very small community of public beta testers. There's quite a few indie games that do the exhibition and game awards circuits for years before release, and then launch with a bajillion "IGF finalist"/etc logos all over their game.

For most game studios and publishers, marketing plans are made right along with the earliest designs and prototypes. Figuring out how to get the game to the masses and estimating sales are critical steps to building a budget.

For a personal project, the best advice I've heard is that you should be a little uncomfortable/embarrassed at your first previews and releases, enough that you need to clearly state it is an early prototype. You'll want to iterate on your marketing plan and launches so that hopefully, after five or ten iterations, you'll be able to solve the flaws in your flow.  Expect to launch and re-launch your product, correcting and improving things each time, repeated multiple times until it succeeds.

Well I will say it simple - as soon as you have something to show