drag the iPhoto library to the trash and empty the trash
But before you do this be very sure you have it on an external drive correctly and that you have a good backup
There is no "undo" to this
Most Simple Back Up
Drag the iPhoto Library from your Pictures Folder to another Disk. This will make a copy on that disk.
Slightly more complex:
Use an app that will do incremental back ups. This is a very good way to work. The first time you run the back up the app will make a complete copy of the Library. Thereafter it will update the back up with the changes you have made. That makes subsequent back ups much faster. Many of these apps also have scheduling capabilities: So set it up and it will do the back up automatically. Examples of such apps: Chronosync or DejaVu . But are many others. Search on MacUpdate
You differeniate between Libraries by naming them differently.
Any way that works - TD suggests several - I use Time Machine hourly (requires an additional hard drive) and Carbon Copy Cloner daily
And note that once you remove the iPhoto library from your computer you no longer have a backup of your old library - you have a single copy on a single disk and when that disk fails (it will someday) you will have lost everything on it)
How to tell them apart - different folders or different names (iPhoto librtary and iPhoto library-old)