First of all, as You've been working with Windows, You have to understand that Ubuntu has totally different way of installing applications. Ok, maybe not so totally, but I will explain it later. Also applications are often different.
Here we mostly use repositories about which You can read here: https://en.wikipedia.org/wiki/Linux_repository . It's generally the 'storage location' from which files are downloaded and automatically installed. They are also used to keep installed applications up to date.
Honestly for me this way is a lot of more comfortable then on Windows. Here You just need to type one command or open Ubuntu Software Center application (Synaptic in future maybe), find application You want, click 'install', type Your password and... that's all You have to do. What's more it also automatically check if there's newer version of application and kindly asks You about permission to update it.
When some application is not available in Your current set of repositories You just add new one to the list. Don't worry now - most of typical applications are in default repositories.
To be honest, while installing application from repository it just automatically downloads correct .deb file and installs it. That means that You can always manually download .deb file You want and install it.
Ok, now answering Your real question.
You can install Wine by opening 'Ubuntu Software Center' from Dash, finding this application, clicking install and typing Your password. That's only one way to deal with it, but I guess that the easiest one.
Anyway the thing is You probably do not really need Wine now. Just type 'filezilla', 'download manager' and anything alse You want in Ubuntu Software Center. There can be some problem with Adobe Air but I believe that if You search about it, You will find solution or alternative.
Hope that helps. :)