If your company has a history of allowing telecommuting, then your conversation will be pretty straightforward. Since there is already a precedent for this practice, you can refer to specific examples or to that particular policy if it exists in writing.
If there isn't a history of telecommuting in your organization, then it's a little less straightforward. But that doesn't have to mean that it's impossible! It just means you will have to put a little more work into making your case.
To actually get your boss to let you work from home, you need to present a detailed plan. You can't just ask, "Can I start working from home?" and expect a positive result. The more prepared you are, the more likely it is that your boss will recognize the importance and feasibility of this option.