So both the Dwemer ruins that I've found so far have been locked. Is this the norm? And if so where do you get the key. When I say Locked I mean the door can't be picked

About half the dwemer ruins are quest related, though most let you in anyway, you may just be blocked at some point further in.

If you find one that won't even let you in the front door without a key it is part of a major quest and you will be sent back there at some point by somebody.

If you're looking for some dwemer ruins to clean out either go hang out on the docks in Riften or in the keep in Markarth.