Some programs will have a specific method. Since no name was given, here's the drill.
1. Place the shortcut to the program in their menu.
2. Give them read and execute rights to the program's files.
If it fails, look up REGMON and FILEMON to monitor what registry and files are being called for in said program. Add read or other access rights as need be with those finding.
Not a trivial undertaking and why it's always fun.
The last out is to call the software's maker. Some will give you the kiss of death that it only runs with full access. Many games are like this.
How do I allow access to a program in Windows XP for one of my users without giving administarive access?