First of, I will work under the assumption that you want to speed up recovery to get faster results (whether these be aesthetic, endurance or strength makes a little difference, but not much)
Fast results are most easily achived through gruesomely hard training, with proper nutrition, sleep and muscle rest. So make sure you don't overtrain (which is a typical mistake)
Now for the fast recovery, consider looking into kreatine supplements. It is probably the easiest way to promote fast recovery. do a 4-6 week on then 4-6 week off cycle to ensure your body will still produce kreatin itself.
Finally growth hormone is naturally developed in the body. This is called testosterone. Testosterone is mostly produced, when you activate the bigger muscle groups, so make sure to do the core exercises and don't fall for the "i only do biceps" stuff.
Squats, deadlifts, etc, will increase testosteron production the most, so make sure they are in your schedule.
Finally, your body will not grow properly, if you do not provide the proper buildingstones (nutrition).
The easiest approach to this is to overeat (preferably on proteins, but most anything can go really). Sideeffect will be that you will get chubby, while you will also be putting on massive gains, at least if strength is your focus.
Another approach is a low carb diet, heavy on proteins and vegetables. If you do go for carbs, go for low gi ones, as they are much more filling than the high gi ones.
If you however are training for heavy endurance activites, such as ironman or marathons, feel free to go a bit more crazy with the carbs.
Good luck with it.