1. In order to do this, you need to have access to the app, which exists as a .ipa file on your device or computer. If you purchased the app on your computer, it should continue to be visible in iTunes and available to you. Just sync your iOS device and it should appear in the Apps tab in iTunes. If so, you're all set and can skip to Step 7. Just sync it and you'll be able to use it.

2. If you bought the app on your device itself, you should already be able to use it. But you'll want to make sure you back it up to your computer by syncing. Since the app has been pulled from the store, you won't be able to redownload it from your account, so if you delete it, it's gone forever--unless you back it up. To do that, sync your device. You should be prompted to transfer purchases from the device to your computer. If not, click File -> Transfer Purchases. This should move the app to your computer.

3. There are other ways that you may need to move the .ipa file from one computer to another. For instance, one family member might have the app and want to share it with others, but it can't be done because the app has been pulled from the App Store. In that case you need to navigate through your hard drive to the folder that all your apps are stored in.
On a Mac, you'll find this folder at Music -> iTunes -> iTunes Media -> Mobile Applications On Windows, it's located at My Music -> iTunes -> iTunes Media -> Mobile Applications.

4. Find the .ipa for the app you want to share. You can email it or copy it onto a USB drive or other removable storage media. Quit iTunes on the other person's computer. Then transfer the .ipa file to their computer, and drag and drop it into the Mobile Applications folder on their computer.

5. Launch iTunes on their desktop or laptop.

6. Connect their iPhone, iPod touch, or iPad and let it sync.

7. Go to the Apps tab and search for the app you want to install. It should appear. Check the box next to it and resync to install it on their iOS device.

8. With this done, if you click the Apps menu in the left-hand sidebar tray in iTunes, you should see the app in the list of all the apps on your computer.