The script provided in the multibib documentation is Unix-based, so we will have troubles running it in Windows. In the script, there's also another command running inside single quotes - basename $file .aux - which returns the full path for $file (which is the current element in the for loop).
The solution is to manually run these commands in the following order:
pdflatex mydoc
bibtex mydoc
bibtex sec
pdflatex mydoc
pdflatex mydoc
As Mico suggested in the comments, you can also create a Windows-equivalent batch file. It's been a while since my last Windows batch file, but I'm almost sure we can use this one:
@echo off
FOR %%A IN (*.aux) DO bibtex %%A
Save it as myscript.bat. It will run bibtex on all .aux files in the current directory. Now, I think TeXworks might not run the batch file in the current directory, so we need to change things a little:
@echo off
FOR %%A IN (*.aux) DO bibtex %1\%%A
and then make TeXworks call myscript.bat with $directory as argument (note that $directory is a TeXworks variable which expands to the absolute path to the directory containing your root document).
Another suggestion (and sorry for tooting my own horn here) is to use arara to automate your document compilation. The header would be:
% arara: pdflatex
% arara: bibtex: { files: [ mydoc, sec ] }
% arara: pdflatex
% arara: pdflatex
\documentclass{report}
...
The secret here is the second line containing the bibtex directive. arara will run bibtex on mydoc (your document name), and also on sec.
Sorry for not providing screenshots and more info, I'm away from my Windows machine right now.
Best Answer
If you use MiKTeX, open the MiKTeX Package Manager aka mpm and choose to install the algorithms package. It contains the algorithmic package.
If you use TeX Live, do the same with the TeX Live Manager aka tlmgr.
Each of these programs should be available in the Windows start menu if the corresponding TeX distribution has been installed.