The simplest method to install things is as follows:
- Connect the new drive to a USB to SATA adapter
- Partition and format the "external" drive using Disk Utility
- Download the OS X installer you want and install the OS on to the "external"
- When you boot to the external, let migration assistant copy everything to the "external"
Test that the "external" works properly, then and only then, make a final backup of the internal drive and swap the hardware.
The benefit of this method is not only that you keep your system unbroken while you test the OS and migration, you can know if you have a working drive and OS without needing to do any "wrench work".
You could use Disk Utility to simply clone the existing drive onto the SSD, but I prefer a clean install to let the OS place the OS files in the proper place and who knows what errors have crept into the existing system over time. Migration is really solid (it wasn't as robust 5 years or more back, and people rightly wanted to clone a working system more regularly then.) You could also use SuperDuper or Carbon Copy Cloner to do the duplication, but again - I really prefer a piecemeal, reinstall as it works best for me time and time again.