Like its predecessors, Windows 10 has a compatibility mode to allow users to run older programs written back when previous versions of Windows were the newest operating system. Right click on the app. Select "Properties". Click the Compatibility tab. Under the banner, a check box will appear next to the text "Run this program in compatibility mode for:" with the options in a drop down menu. The various Windows operating systems will appear, depending on the app.
A more involved option is to install a virtual version of the old operating system of your choice ("virtual machine" or "VM") on your computer. This is different than dual-booting a computer, where the user divides/partitions the space on a single hard drive and installs a different operating system on each section, allowing the user to choose which OS is booted when the computer is powered on.
The advantage with VM is the ability to run a program in the operating system that it was designed for in the first place. Windows 10 is compatible with Microsoft Virtual PC, a virtualization software that allows Windows users to run multiple versions of Windows, all the way back to Windows XP. This is a free download from the Microsoft Download Center.
Microsoft provided a free copy of Windows XP to run in Windows 7 Pro. Pro versions of Windows 8.1 include Hyper-V to host alternative operating systems. Otherwise, Oracle's (formerly Sun's) VirtualBox and VMWare are some of the more common options available and are accessible for Windows, Mac and Linux users. Mac users can also use Boot Camp and Parallels to access alternate OS versions.