This may help you with intellisense and possibly other Visual Studio integration problems:
Sometimes the fix is as simple as doing Assets → Open C# Project from Unity. Other times it requires more.
Other times it requires you also nuke the userprefs and .vsconfig and other crufty low-value high-hassle files that Visual Studio tends to slowly damage over time, then try the above trick.
Barring all that, move on to other ideas:
Also, try update the package inside of Unity: Window → Package Manager → Search for Visual Studio Editor → Press the Update button
Update: The VSC extension has been deprecated.
There is a community fork available that is receiving updates.