Take stock of what's in the backyard and research the historic significance of the home and property before making any changes. Mature shrubs and trees worthy of preservation can be tagged for keeping, perhaps looking to a local university horticulture department for assistance identifying old-fashioned cultivars and heritage specimens. Making a map of the key features helps to begin the process of piecing them together into a future design. All weedy species that may have taken over parts of the yard should be removed to see what lies beneath.
Mature trees need special attention to make sure they are structurally sound and are not a risk to life or property when the wind blows. An arborist can help to assess their health and take steps to remedy those in poor condition or recommend removal, if necessary. Pruning and shaping and the removal of dead or diseased wood will almost certainly be in order for many of the older plants. For others, regular waterering, top-dressing with compost and applying a fresh layer of mulch will bring them back from a neglected state.
Old brick patios, stone borders, filled-in water features and other treasures may be hiding underneath the overgrown vegetation -- and sometimes under a shallow layer of soil that has accumulated over the years. If these relics are found, consider if any should be restored and used in their current location. Vintage bottles and cans, tools and toys may also be unearthed. If these have historic value and visual appeal, use them to decorate the garden. Talk with a local librarian or archivist about the previous use of the property for clues on the origin of any found objects and materials.
Old cans and containers can become pots and planters, while tools, toys and other trinkets can be recycled as parts of birdhouses and other "garden art." Perhaps there is old wood or scrap metal that can be artistically combined in a trellis for a new vine. If old brick and stonework is not suitable for using where it lies, pull it out and reconfigure the materials to fulfill another purpose. Finally, even the overgrown plant material can be put to good use -- renting a chipper-shredder for a day can provide a pile of mulch to make the reclaimed landscape look extra neat and tidy.