Fencing or other suitable barriers are by far the most effective in protecting gardens from animal damage. Unfortunately, these also are the most costly, in initial time and money required to install. Over the long term, these costs can be worth the effort compared to other methods.
Birds: install screening, overhead lines, or netting like the ones pictured below.
Ground Animals (non-climbing): install fences with walls at least 24 inches high, and a skirting buried 2 inches below the soil and bent away from the area that needs protection. The skirting should extend at least 18 inches from the base of the fence (to prevent digging). Pay close attention to gateways; you don’t want an animal to crawl under the gate. Take snow depth into consideration when you decide how tall to make the fence.