I have recently bought a new pc which came pre-installed with Windows 8 (no DVD).

PC came with a regular HDD however I have purchased a SSD and I want this to be my primary drive and to run the OS on this. I am just confused as to how I will get windows 8 onto this drive as I have no DVD

Am I able to create or download a DVD of windows 8 that I can use to install the OS on my new drive and will my product key from pre-installed windows 8 work with this? I'm just worried it won't work as it has already been used??

You will have to create a recovery drive which you will have to use to reinstall on the SSD:

Press Windows key + W
Type: create recovery drive
Hit Enter
Follow on the screen wizard.
Make sure you get a thumb drive with at least 16 to 32 GBs of space
Make sure the option copy recovery partition is selected.
After the backup is complete, you can use this reinstall Windows 8 on the SSD.