I want to see the amount of traffic that is in both "Segment A" and "Segment B". Can I do that in Google Analytics?
Yes this is called a multi-segment view.
To apply Segments to a report: Sign in to your Google Analytics account. Open the View that includes the reports you want to use. Click the Reporting tab, then open the report you want.
For example I will use Audience Overview report. At the top of your report, click + Add Segment...