Running with a jogging stroller takes some time to get used to. If you have not tried one before, a great tip is to take it out for a spin for the first time, sans baby, just to get the feel. Most jogging strollers are made to easily roll along a flat surface and therefore, it becomes vital to lock the brake on even the smallest of hills when stopped. Some have hand brakes by the handles and some have a foot brake.
Before running, become familiar with the various components of the stroller. Some strollers have handles that may be slightly adjusted up or down for better reach and proper posture. You will want the handles slightly higher than elbow height when you reach out to grab the stroller. Another option is to use the safety grab strap to hold and see the height you are comfortable holding the strap at. You’ll likely want the handle a little higher than that.
When running, the stroller should be slightly in front of your body and plan to run holding on with one arm at a time (elbows slightly bent), and switching throughout the run, as one side fatigues. It is better to switch so your body develops some equal strength on each side of the body. Some strollers require a hand on the handle to lift and turn so plan accordingly on the path you are using.
Running posture should include a very slight lean in the trunk much like you would when running normally. Avoid leaning or putting weight at all on the handles or you will find yourself leaning more forward. Knee lift will be slightly lower. One or two arms swinging (with safety strap) should be similar to regular running and you will probably have to shorten your stride a bit with the stroller in front of you.
Yes you can run hills for strengthening, speed work (it won’t be quite as fast) while pushing a stroller so let your heart rate be a good gauge as to how hard you are working. When running uphill, avoid leaning too much on to the stroller handle. Downhill, be sure to use a safety strap and hand near the hand break if one is provided. Of course, this is for when baby or your child is a more experienced stroller rider and is able to sit up easily on their own. Enjoy and happy stroller running.