Answer: Without knowing what the shrub is it is hard to give you hard and fast pruning instructions. However, in most cases the best time to do renewal pruning on a badly overgrown shrub is late winter/very early spring. The spring pruning will sacrifice some flowers, but the size and health of the shrub are improved.
Since we don't know what the shrub is, I would suggest a somewhat conservative three year plan for the renewal pruning: each year for three years cut out a third of the oldest stems. Cut them as close to the ground as you can. After three years, you will have removed all of the old overgrown wood. In response to this pruning, the shrub will probably send up lots of suckers. Thin many of these out from the base, too, leaving a well-shaped shrub.
Most of the big old flowering shrubs are "survivors" but they do appreciate a good dose of balanced fertilizer or well rotted manure in early spring and will appreciate some extra water in case of drought. Good luck with your shrub!
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