Was asked to develop a QA process for small projects (<$50 K). How do I go about this?

I assume you don't have any existing QA processes at your organization and you were asked to develop all the processes from scratch.

This depends on how much money your organization is willing to spend writing processes.

Before start writing processes, a plan needs to be published if it does not exist. You may want to consider proposing to your managment to recruit professional QA experienced in writing processes and/or CSQA to assist you in writing the processes.

For anything you do, just follow PDCA cycle.

P- Develop a plan and get approval
D - Write processes based on documented plan/scope. Pilot these processes
C - Monitor and Control process results
A - Improve these processes.