Before start, we should ensure that client script debugging is not disabled in IE as it is by default. Suitable options are located on Advanced tab of Internet Options where both script debugging checkboxes should be unchecked.
We can come back to Script Explorer. As it was written before, it appears only while the debugger is working. So after starting project we can go do Debug->Windows where should be Script Explorer. Sometimes, don’t know why, it doesn’t so in this case we have to find it manually. Staying in debug mode right click on tool bar and go into Customize. Then select Debug in Categories on the left side of window and find Script Explorer on the right. Just drag it to Debugging toolbar.
At this moment, we can debug it in well known way using breakpoints, steps, Watch and QuickWatch, just like in the server side, including context browsing of a variable.
Breakpoints can also be set up in external *.js files before project will be loaded. Then, after loading project, the breakpoint will be activated by debugger. Note, that it is only possible to *.js files not for scripts embedded in pages. These scripts are available for debugging only after loading page.