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?
I'm almost sorry that Amazon offers SQS as a service. It is not a "simple queue", and probably not the best choice in your case. Specifically: 

it has abysmal performance in low volume messaging (some messages will take 90 seconds to arrive) 
message order is not preserved
it is fond of delivering messages more than once
they charge you for polling

The good news is it scales well. But guess what, you don't have a scale problem, so dealing with the quirky behavior of SQS is just going to cause you pain for no good reason. I highly recommend you check out RabbitMQ, it is going to behave exactly like you want a simple queue to behave.
How should Amazon SQS be used? Import / Process Scenario