To "make a go of it" means to try something that seems a little challenging and will have a major effect on your life. For example, you can use this phrase when:

• you're moving out of your parents' house for the first time
• you're going to move to a new country
• you're getting married
• you're quitting your job so that you can change to another, more interesting, career

Here's an example:

After I graduated, I wasn't sure what to do, but I always wanted to try acting. So I moved out to Hollywood and made a go of it.