If you know how to use DOS, try opening DOSBox first, then mount some drives and navigate around inside of it to run the setup program and then the game. Drag'n'drop makes it harder to see what the problem is.

1. Create a directory for your game, e.g. "C:\DOSBox stuff\Warcraft".
2. Insert CD in drive.
3. Start DOSBox.
4. In DOSBox, mount up DOSBox's drive C: and D:
   
   Z:>mount C "C:\DOSBox stuff\Warcraft"
   Z:>mount D "D:\" -t cdrom -ioctl
   
   (assuming that D:\ is your real CD/DVD drive)
5. Install the game from D: to C:
   
   Z:>D:
   D:>install
   
   (or whatever the command to start the installation is called. Check your Manual/Installation Guide for Warcraft for the exact command to use)
6. Configure sound, configure graphics, ...
   
   D:>C:
   C:>dir
   C:>setup
   
   (when you configure sound and are asked about stuff like IO/IRQ/DMA/High DMA addresses, please verify that you use the same values as listed in "%ProgramFiles%\DOSBox-0.63\dosbox.conf")
7. Start game.
   
   C:>warcraft
   
   (or "run", or "play" or whatever the command to start the game is called. Check your Manual/Installation Guide for Warcraft for the exact command to use)

Thanks so much MiniMax!

warcraft is a bit tricky as the installer(setup.exe) doesn't work in 0.63

so you get into a loop. stating that you should run setup.exe but that doesn't work

try downloading the version available here:
http://cvscompile.aep-emu.de/

Thanks Qbix - I wasn't aware of that little gotcha 🙁

CD version of Warcraft 1 installs and plays perfectly for me in DOSbox 0.63 😖

The only odd thing is the speed. The animations and briefing parts need low cycles, but while playing I need higher cycles.

Johan: which core are you using? (simple/normal/full/dynamic)

Dynamic, but it works too with normal, full, and simple.

I've been toying with my config, and i've found the solution. In my config, I had the "-ioctl" option in the mounted CD-ROM (I recommend to use it always, it hasn't caused me any trouble and fixes many things 😀). Without it, the installation hangs when it starts copying the files.