I prefer to use AppSettings myself but for your purposes I imagine straight ConnectionStrings per the above link will be just fine.
If you are not familiar with the app.config/web.config files, it is worth your while to walk through some tutorials. They make life a little easier.
Note this method will leave your connection strings sitting around in a plain text file. If that bothers you then you'll need to get a little more creative, such as storing the encrypted strings in an appSetting and decrypting them when needed. I won't go there right now, just be aware there are options once you get the basic idea.