How do I install FCPX on a second computer?

If you've already bought it, just sign in to the AppStore again with the same ID and download it. You won't get charged again.

Excellent , Thanks. Had the same question. I assume it can be installed on as many Macs as one owns?

Morning! here are the steps:

1. Open the Mac App Store.
2. Click the Purchases button in the Mac App Store toolbar.
3. Sign in to the Mac App Store using the Apple ID you first used to purchase Final Cut Pro X.
4. Look for Final Cut Pro X in the list of purchased applications in the App Store. If you don't see FInal Cut Pro X in the list, make sure that it's not hidden. See Mac App Store: Hiding and unhiding purchases for more information.
5. Click Install to download and install Final Cut Pro X.

Thae Mac App Store license allows you to install it on any number of devices you own and control, assuming this is an individual purchase.

-ShinerMac

You don't even need to waste time downloading it.

Simply copy it across to your other computer using a memory stick or hard drive etc..

Yes....

MAC APP STORE PRODUCT USAGE RULES

Except as otherwise set forth herein,

( i ) If you are an individual acting in your personal capacity, you may download and use an application from the Mac App Store (“Mac App Store Product”) for personal, non-commercial use on any Apple-branded products running Mac OS X (“Mac Computer”) that you own or control.

Source:
http://www.apple.com/legal/itunes/us/terms.html#SALE

-ShinerMac

Thank you this was perfect solution...