Nowadays, I just...don't watch trailers. I try to go into films with zero expectations and as little knowledge about the film (other than casting news here and there) as possible. It makes the experience much more enjoyable, and allows me to be a bit more relaxed in my fandom.
This is the crux of "burnout" in my opinion. With the vast online communities available and the media saturation of content, there's no anticipation, no long term goal. I already see a bunch of people saying, "Well, I marathon'd my way through
Daredevil, now what?" Why would you do that to yourself? As a fan, don't you want to savor this thing you've been anticipating for months?
Another great example is
Avengers: Age of Ultron. Between the multiple trailers, TV spots, released clips (e.g. Hulk vs. Hulkbuster), and behind-the-scenes featurettes, I bet a third of that movie is already available or revealed. It makes the actual watching of the thing less enjoyable because we've seen so much of it already.
I have actively avoided most of the stuff on
Avengers: AoU, save for the trailers and whatever TV spots happen to come on while I'm, y'know, watching TV. I have also only watched the first 2 episodes of Daredevil; me and my roommate are watching about 2 episodes a week, with a few days in between each, looking forward to it like we would an actual television series. It makes it much more fun, if slightly frustrating, to build up anticipation and then be wow'd when we finally get to watch.
My advice to anyone experiencing burnout: step away. Don't remove yourself completely, but maybe just sit on the edge of the pool rather than submerging yourself in the deep end. If you are burnt out on Star Wars, don't visit the dedicated forum here, and avoid the topic on the movie in the "Entertainment and Movie Talk" forum. Same goes for Marvel, or DC. You fell in love with them for a reason and if you remove ourselves from the constant bombardment of spoilers, media chatter, and reveals, you'll probably end up missing them and rekindle that joy.