The traditional solution for many businesses will be to try to put some kind of management or endpoint security app on employee-owned devices. But this can lead to a slippery slope of supporting employee devices. Because you know that once you put that app on their device, IT will be to blame for every problem that comes up on that device.
From an employee standpoint, this is also a big problem. Do you really want some app with remote monitoring and management capabilities sitting on your personal device? And do you really want to give someone else the ability to remotely wipe all of your personal data and information?
Luckily, we are starting to see some more creative methods for handling this problem, including strategies such as using virtualization to separate company apps and data from personal apps and data, as well as methods such as HTML 5 gateways to provide remote access to company applications.
For now, probably the most effective method is education. Setting down policies on how employee-owned devices should and shouldn't be used in the work environment can hopefully head off the worst problems.
Of course, the solution that some companies will choose to follow is to ban the use of employee-owned devices. But this has very little chance of success. If employees can use the device they prefer to use, than they will. Businesses will have to learn to deal with, and manage, this new reality.