How to Install OS X on new hybrid hard drive

You'll almost certainly need to format the new drive first.The normal way to this is by using Disk Utility, the free repair utility Apple install in the Applications/Utilities folder.

When you attach the new drive in an external USB/FireWire/Thunderbolt case, the drive mechanism will appear in the left-hand panel in Disk Utility. Select the drive icon, and the Partition tab will become clickable. Click that tab, and partition the new drive as a single OS X Extended (journaled) partition. Depending on what version of OSX you're booting from, you may also see an Options button. If the Options button appears, click the button and select GUID Partition Table, which is required for installing a bootable OS for Mac/Intel systems.

Once the disk is formatted, you can either install an OS of your choice on it, or clone your existing drive data to the new drive using a third party utility such as SuperDuper! or Carbon Copy Cloner*. This will copy all the data from your existing drive onto the new drive, and then make the new drive bootable. At that point, you open up the machine and swap the drives.

If you've been having any kind of odd software behavior, a better option is to install a clean operating system on the new drive, boot off the new OS on that drive, and transfer your applications/user accounts to the new drive using the Migration Assistant stage of the setup process. About halfway into the first boot off a new OS, the setup assistant will ask if you want to transfer data from an external source - a different drive, a different computer, or a Time Machine backup. Select "other drive", and the assistant will allow you to select the user accounts/applications you want to move over. This will leave behind whatever OS oddities were on the old drive, so you can get on with developing new OS oddities.

*It's also possible to clone a drive using Disk Utility; but it's a fiddly operation, and Disk Utility will quit for trivial reasons. The shareware utilities I've listed above are far more straightforward about what they're doing, and more reliable as well.