Implies a determined attempt despite challenges. They're really making a go of their small farm despite the tough weather.
Pro Tip 2/3
Success Oriented
Usually used when there's a hopeful attitude towards the success of the undertaking. She's going to make a go of her online store, optimistic it'll succeed.
Pro Tip 3/3
Not Casual
Suggests a serious and committed attempt, not just a casual effort. The team decided to make a go of the project, devoting all their resources.