Swing your arms more across your body to help keep your balance and to rotate your hips to improve stride length. Keep weight forward by having your hips over the landing foot. Concentrate on using the muscles in the backs of your legs and coming up off your back toe to push you forward. Remember you can go a lot faster than you think and still be under control. You must concentrate on relaxing and metering out your energy over the hill.
Many hills are steepest at the bottom and flatten out near the top.
A well walked hill has you picking it up at the top and into the downhill transition. A short quick stride helps supply more fuel and oxygen than a long slow one. This is the same reason that it is more efficient to use low gears and fast cadence when riding a bicycle uphill rather than high gears and a slow cadence. If you don't believe this, try walking downhill with a pulse rate monitor and notice how much faster you can walk at the same pulse rate than on the flat. Work on increasing stride length and using your arm swing for balance.