How to go about something means how to begin dealing with it. After go about, use a noun or an -ing form: How do you go about fixing a flat tire?
How do you go about applying for a visa? asks for the first steps you would take, not whether to apply.
How it sounds in real life
A small leak appears under your sink, so you message a friend: How do I go about fixing this myself? You are not asking whether the pipe can be fixed. You want the steps, where to start, and what to do first.
A friend forgets a birthday and feels awkward. She says, I wasn't sure how to go about apologizing. She knows the apology itself matters; she is stuck on how to begin it.
Not the other 'go about'
Go about has a second, unrelated meaning: doing your usual routine or moving from place to place, as in She goes about her business. In questions like How do you go about getting a permit?, it means tackling a task, and the listener understands it as a request for the steps.
The same phrase can also mean moving from place to place or doing your usual routine: She goes about her business.
In how to go about, the meaning shifts to dealing with a task: How do you go about getting a permit?
Context makes the difference. The permit question asks for the steps to follow, not for wandering around town.