I think we can all start with the little things, such as bringing reusable cutlery (titanium spork, anyone?), a pouch for waste and of course, a water bottle.
While hiking

, always keep to the marked trails, respect the land and leave no traces of your adventure behind. Needless to say, don't feed the wild animals, even if they are oh so cute. This includes fruits, as they may not be part of their native diet.
If you are camping

overnight, particularly at a site without a toilet, do bring a small shovel to bury your waste responsibly. Note that toilet paper should not be buried but bagged away to be taken with you when you leave.
When washing up (yourself or your cutlery), keep detergent/shampoo/soap out of water sources such as rivers/streams/lakes.

Let's all do our part to look out for the environment!