AppleWin / load & run program

I'm an absolute beginner in Apple IIe world.
I use AppleWin emulator for Windows.
I loaded a virtual diskette into floppy 1 and guess a command "CAT".
But, how can I load and run program from that diskette?

The "original" OS was called DOS, the most common variant is DOS 3.3. The "later" OS was called ProDOS ( Professional DOS ), which allows Sub-directories among other features..

DOS has the CATALOG command.
ProDOS has the CAT command for a 40 Column Catalog and CATALOG for an 80 Column CATALOG

To LOAD and RUN a BASIC Program from the Diskette, Type, "RUN FOOBAR", with FOOBAR being the Name of the Program. For a Binary Program, use "BRUN FOOBAR2", with FOOBAR2 being the name of the Binary Program.

See these manuals for more instructions:

Apple DOS 3.3 Manual

Apple ProDOS Manual

If CAT works, then you're using ProDOS. In ProDOS (only), you can use the minus character (-) to automatically run any executable type of program, no matter if it's a BASIC or System program. So, for example:
-MYPROG
will run MYPROG for you.