How to show inferred TypeScript type in WebStorm?

Although not perfect. Press the Ctrl key (or ⌘ Cmd on macOS) and hover over a variable with the mouse to kick in the inference logic in webstorm :

Assuming the cursor is already on the variable the best way is:

1. Ctrl + Shift + P
2. Return

Starting from WS2017.2 Ctrl (Cmd) + Hover shows inferred type.

Also you can try Quick Documentation: Ctrl + Q ( F1 for OS X )

Updated: in 2020.1 it will work as a part of the quick documentation and it works on hover if Preferences > EditoGeneral > Show quick documentation on mouse move is checked

Late to the party, and not sure when this came out, but there is a setting:

Show quick documentation on mouse move. Delay: [500] ms

Where delay is editable.

You can get to it by

File -> Settings -> Editor/General -> #Other / Show quick documentation on mouse move

Works similar to VS

Depending on the context, there are different ways to get type information. (Shortcuts for OS X)

1. View > Expression Type ⌘⇧P: shows a popup
2. Navigate > Type Declaration ⌘⇧B: navigates in the editor
3. If 2. does not help, I do Navigate > Declaration ⌘B and then 2.
4. View > Quick Definition ⌥Space (or ⌘Y)
5. View > Parameter Info ⌘P: shows a popup with the declaration of a function parameter