I played Call of Duty Advanced Warfare on my friend's PS4 and logged into my PSN account. I have now got a PS4 and the game myself and was trying to figure out how to get the progress I have achieved on my friend's PS4 onto mine?
If you're talking about progress in the single player campaign, game saves are stored locally on the console. To transfer them from your friend's PS4, plug in a USB-Stick or external hard drive and in the main console menu go to
Settings > Application Saved Data Management > Saved Data in System Storage > Copy to USB Storage Device
There, search for your Advanced Warfare save files and copy them to your storage device. Then plug it in to the other console and go to
Settings > Application Saved Data Management > Saved Data on USB Storage Device > Copy to System Storage
and copy the files onto your own console. It's important that you are signed in with your own PSN account when you copy the files from your friend's PS4, because according to the PS4 User's Guide you need to have signed in at least once with the same account you used when you copied the saved data.
If you have an active Playstation Plus subscription, you can also upload your save data to your cloud storage and download it on the other console. To do so, follow the same steps as above, but instead of copying onto a USB device, select "Upload to Online Storage" on your friend's console and "Saved Data in Online Storage" when copying the data to the other one.
If you're talking about online progress: Your multiplayer progress in Advanced Warfare is stored on game servers online and are automatically associated with your PSN account, so you don't need to transfer save data for it manually.