Here is the picture of the bush.
There are some important considerations in pruning any shrub: what and how much to prune, and when to prune.
In your case, since you don’t know what type of shrub you have, and it is not possible to tell from this winter photo, the best advice would be to wait until your shrub blooms and you can identify it. This is important because some shrubs bloom on old wood, which means that their flowers appear on stems that were produced during the previous growing season. If you prune these shrubs in the spring, they will not bloom. They should be pruned after they flower. Here is an earlier Toronto Master Gardeners post that explains this aspect of pruning and offers much other good advice on gardening practices: http://www.torontomastergardeners.ca/askagardener/spring-cut-backs/
In general, if you want to tidy a badly overgrown deciduous shrub, you can remove up to a third of the oldest, thickest stems every year, cutting them at ground level. This will invigorate the shrub and will promote growth of new stems. This is known as “renewal pruning”.
Another technique for pruning old and overgrown shrubs is “rejuvenation pruning” which involves cutting all stems back as close to the ground as possible in the early spring, which of course means sacrificing any blooms, but will allow the shrub to regrow like new. This technique has better results on certain shrubs such as forsythia and spirea.
Here is a link to a brief illustrated guide that may help you: http://www.mortonarb.org/trees-plants/tree-and-plant-advice/horticulture-care/pruning-deciduous-shrubs