Warm-up: Going uphill will workout your muscles, it is best to plan on warming up with a walk on the level for 5 minutes before you tackle a steep hill.
Shorten Your Steps: Like a bike shifting to a new gear to go uphill, shorten your steps.
Maintain or quicken your step rate: With shorter steps, you won't be going as far with each step. You can maintain your step rate, knowing it will take a bit longer because of the hill. Or you can try shorter, quicker steps on the hill if you want to maintain your pace.
Leaning: It is natural to lean into the hill a bit. Try to keep that lean to a minimum, keep your torso over your hips, if you lean too much you put yourself off balance. Do not lean backwards, that will unbalance you. Leaning too far forward or leaning back can strain your lower back.
Your Knees: You shouldn't be lifting your knees higher than 6 inches, if you are then you need to shorten your step even more.
Exertion: Hills will raise your heart rate, breathing, and exertion level as more muscles are used to carry you both up and along. Keep your exertion at an intensity where you can still speak in sentences rather than just gasping out single words.
Heart Rate: Hills are a good way for slower walkers or highly fit walkers to achieve a higher heart rate level. Check your heart rate on hills to see what various rates feel like for exertion and breathing intensity.
Jones, AM, JH Doust. "A 1% treadmill grade most accurately reflects the energetic cost of outdoor running." Journal of Sports Science 14(4)(1996): 321-7.