I had a fairly hard time getting WINE running on puppy linux but OK. I assume you are running a stock version rather than a puplet (some of them already have wine)
The way I did it.
Wine is technically not based on slackware linux but it retains a close enough link to use programs, note while you can do this I do not suggest it for graphical apps or ones you want on the start menu unless you want to add it yourself and if you can do that you might as well compile it yourself. "invisible stuff" like WINE is OK though.
Wine in slackware form from the wine sourceforge page:
http://sourceforge.net/project/showfiles.p...package_id=6301
Note I only suggest this over the actual puppy linux builds as they take a while to update and wine is really one of those things you want the updates for.
You need to convert them, you use the tgz2pet command. Note this is designed for slackware tgz files, "normal" tgz files are unlikely to do anything with this.
This will make a pet file (the puppy linux package) that you can install, it will probably say something about lacking libraries but it should still work.
Next up comes getting wine to activate.
The way you are supposed to do it is to launch a command line (the ` button, next to the 1/! button on the keyboard gets you one)
The you type
wine somefile.exe
where somefile.exe is the file you way. Remember the autocomplete function of linux command line when you are using this (the tab button)
You can also make it so exe files will autolaunch with wine. Know however that doing this will block the info the command line may give you which can help with bugfixing (long story short WINE is an implementation of the windows API that is to say functions that windows allows a computer to perform are copied by WINE, they are not copied perfectly however and many times you can boost compatibility by giving the program some actual windows files rather than relying on what WINE can do, not command line means not knowledge of what might have gone wrong), of course you can still launch with the command line for such situations.
I forget the exact steps but you can add it wherever you choose what puppy linux does with a given file type (simply put wine in the first part of the command line section)
As you came from a virus laden machine know that doing it the latter way along with the every user is root feature of puppy linux is not all that secure, probably still more secure than basic windows but far from ideal.