I want to co-ordinate telling Server B to start a process from Server A, and then when its complete, run an import script on Server A. I'm having a hard time working out how I should be using SQS correctly in this scenario.
Server A: Main Dedicated Server
Server B: Cloud Process Server

Server A sends message to SQS via SNS to say "Start Process"
Server B constantly polls SQS for "Start Process" message
Server B finds "Start Process" message on SQS
Server B runs "process.sh" file
Server B completes running "process.sh" file
Server B removes "Start Process" from SQS
Server B sends message to SQS via SNS to say "Start Import"
Server A polls constantly polls SQS for "Start Import" message
Server A finds "Start Import" message on SQS
Server A runs import.sh
Server A completes running "import.sh"
Server A removes "Start Import" from SQS

Is this how SQS should be used or am I missing the point completely?
What you laid out will work in theory, but I am moved away from putting messages directly into queues, and instead put those messages in to SNS topics, and then subscribe the queues to the topics to get them there - gives you more flexibility to change things down the road without every touching the code or the servers that are in production.
For the what you are doing now, the SNS piece is unnecessary, but using will allow you to change functionality without touching you existing servers down the road.
For example: needs change and you want to add a process C that also kicks off every time the 'Start Process' runs on Sever B. Right thru the AWS SNS console you could direct a second copy of the message to another Queue that previously did not exist, and setup a server C that polls from that Queue (a fan out pattern).
Also, what I often like to do during initial rollout is add notifications to SNS so I know whats going on, i.e. every time the 'start process' event occurs, I subscribe my cell phone (or email address) to the topic so I get notified - I can monitor in real time what is (or isn't) happening. Once a period of time has gone by after a production deployment, I can go into AWS console and simply unsubscribe my email/cell from the process - without every touching any servers or code.
How should Amazon SQS be used? Import / Process Scenario