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?
Well... SQS doesn't not support message routing, in order to assign message to server A or B that why one of the available solutions: create SNS topics "server a" and "server b". These topics should put messages to SQS, which your application will pull. Also it possible to implement web hook - the subscriber on SNS events which will analyze message and do callback to your application.
How should Amazon SQS be used? Import / Process Scenario