The obvious areas to strengthen for hiking are the legs, and lets face it, they are carrying you and your gear to where you need to go.
For starters, start walking.(or running)
Depending on your fitness, start slow and give yourself time. this is not a good game for those who jump in. You can tell who they are on the trails – sad, blistered, and grumpy. Don’t let that be you. You are a happy person who enjoys strolling in the hills.
If you are not lucky enough to live near the mountains, I like to figure you should look at your expected daily mileage on a trail and add 3-5 miles for elevation and a pack. If I expect to pack 5 miles a day, I like to able to walk 10 easily. If you are expecting 15 miles a day, I would hope you have a rigorous plan in place and are not just leaping off the couch. Running, for me, is helpful for those kinds of miles.
Get on uneven ground
You need a “proprioceptor enriched environment”. The most obvious injuries in hiking and backpacking are ankle injuries. You can compensate for training on flat ground or machines by wearing huge supportive boots, or you can strengthen your ankles and stabilizing muscles and wear something more comfortable. I would suggest the later, though if you have already tweaked and wrecked your ankles, boots that help support your ankles may still be a good idea.
Ask yourself before you start: How stable am I? If you are active and fit, start doing your runs and walks on local trails, stairs or even rocks by the shore. If you need more build up to this (and don’t lie to yourself about this or you can get hurt), work on stabilization exercises in a safe environment first and then get outside.
How and where would you do this? Get a trainer. And read up on it. Proprioception, simply put, means sense of self. The proprioceptors are sensors that provide information about joint angle, muscle length and muscle tension, which gives the brain information about the position of the limb in space at any given time. When your stabilizers are strong and your brain used to dealing with the information and reacting well, then hitting the trails will be a lot easier.