You cannot use the CMIS API against the Alfresco Cloud just yet. A public cloud API has not yet been released. We hope to have that for you soon, though!
That's too bad. I visited this site specifically to get the answer to this question. Adobe recommends Alfresco as its DAM of choice because of its CMIS integration specifically with Adobe Drive, an integral piece of its creative suite tying multiple tools (Photoshop, Illustrator, InDesign, Bridge, etc.) together. My company has also integrated its own Enterprise solution to be CMIS-compatible and Alfresco (our own on-premises version) was our main test bed. I was very excited to see a polished cloud-based Alfresco set up here. However, without CMIS this cloud service is little more than a pretty toy.
At the moment, as far as I can tell you cannot connect adobe drive to the Alfresco cloud CMIS API because it requires OAuth and Adobe Drive does not, again from what I've seen, support that authentication.
I am just evaluating Alfresco in the cloud using Alfresco free offering (my.alfresco.com). I don't find the information how to connect to my content via cmis.
But you'll need an API key to hit that and you'll need to use OAuth2. All of which is documented on http://developer.alfresco.com and in the examples linked to earlier.
