Hill training is actually very intensive and not something to step into without knowledge. This is of course if you are looking to really increase and up your training.
First you need to incorporate a good
strength training program with a focus on deadlifts ,Step-Ups, and Lunges variations. (Power lunges, rear lunges, walking lunges). Focus on power, speed and endurance.
I would incorporate
HIIT in a weekly session and then I would focus on specific hill training. Some movements that go beyond running up and down a hill would be...
-Sideways hops (moving up and down the hill in sideways)
-Backwards-This helps incorporate better balance and stabilization
-Hop forwards
More than just training you need to focus on a few aspects WHILE training.
-FOCUS your breathing, do not breath to heavy, do not let your oxygen disruption come from impact.
-Incorporate a smart stretching program. Dynamic movements pre-run and static post. Also work with foam rollers to lessen injury or tight muscles.
-Keep your posture form perfect, keep your arms tucks in. Don't use them to get you up that hill, you will likely injure your back. Point being run in good form even if slower.