I get on and off shin pain just in my right leg. Bad enough in the past it's stopped me from running for 8 weeks but pretty much under control at the moment. Exercises that are supposed to help are toe tapping and eccentric calf loading - you can prob find both on youtube. I never noticed much difference doing them but then again my shin IS better than it was last year so I guess they probably did help.
I also go for regular sports massages - every 4-6 weeks - and just having everything in my lower legs eased off seems to make a difference. Tight calves don't help. But really I think the thing that's helped the most has been using a foam roller - for a while there I was using it before every run I did, and also rolling my calves on a tennis ball to target the tight bits even better.
If you haven't had proper gait analysis done yet, go get that checked out. I had to change my shoes for a while - was advised to ditch my favourite brand of trainers for ones with a slightly stiffer sole and heel cup. I didn't like the feel of them on my feet but they definitely helped my shin. I'm still wearing them for most runs but gradually easing back into my old favourites as they're comfier on my feet.
Basically there's no one thing you can do that's guaranteed to help but there are loads of small things that can all add up to give you an improvement...
