You need to add their UUID to your devices list on the developer web site, and then create an 'Ad-hoc' provisioning profile that contains your App ID and their Device ID (any any other device IDs you want). Now build and archive your app from Xcode, and choose 'Ad-Hoc' - if the option isn't available make sure you have a phone connected.
You'll end up with a .IPA file that can be emailed and dragged into iTunes for install.
This creates an app that is as about as similar to a Live app as you can get, so for example Push Notification will need to use the Live Certificate. If you're sending to a client, I would recommend you add one of your phones into the provisioning profile and try the iTunes install on a clean machine and on a phone with no development profiles installed, just to be sure it works.
As mentioned above, you can also use a 3rd party service to do this, but you don't need to and I never have, though it may well be easier.
https://developer.apple.com/library/mac/documentation/IDEs/Conceptual/AppDistributionGuide/TestingYouriOSApp/TestingYouriOSApp.html for full instructions.