To save a search simply name it once you've returned results.  The Name field is above the results total:

Once you type a name, press enter. The system will flash a message at the bottom of the screen confirming the search has been saved. Several things have happened and are now available to you.

First, your options for what you can do with the search has changed:

View Public Link will open a screen showing what people whom you share the link with will see.
Copy Public Link will allow you to quickly paste the link to an email, or Facebook update, or anywhere you might share a link so that people can see the results of this search.
Email Public Link will prompt your computer to open your email program and send the results of the search to an email.
Choosing Print Listings will follow up with a page asking if you'd like to print the Agent View or the Client View.  It will then display the report and automatically prompt the printer.
Make Cloud Stream will load CloudStreams and treat it as a Valet style search to send to your client.

If you go back to the CloudMLX homepage (click on the cloud icon in the upper left corner) you'll see a Recently Saved Searches portion of the page now has that search showing.  This way your most recent work is always visible and avaiable when you open CloudMLX.

Clicking your initials in the upper right corner of CloudMLX you will see the Saved Searches option in that menu.  Choosing this menu item is where you can delete the search if you'd like.

To modify a search, run it then alter the criteria as needed.  Once a change has been detected two options will appear below the search name, above the results:

To accept the changes without renaming the search, click the blue Save Changes button.  If you'd like to keep the original search as is but make this change into a NEW search, click "Save as..." and give the new criteria a different name.