I am hoping to learn how to develope Android Applications but know little to nothing about how to go about the process. I was hoping to hear your recommendations on what equipment (preferrably free if possible) to use as well as the best way to learn go about developing. I am sorry if this question is too broad.
The first thing to say is that Android Applications are written in Java, so if you don't know Java, you should learn that first before starting with Android Development. You'd want to be familiar with Java fundamentals - classes, methods and so on - before you started with your Android application.
You can download the Android SDK for free. This comes with documentation and an emulator so you can test your application on your PC without any need for a phone. There's also a tutorial which is a good place to start (assuming you know Java).
As for places to get more information, the Android Developer's Blog has just recommended Stack Overflow for Android newbies (so well done for coming here!) and there's the android-developers Google Group once you get up to speed.
Regarding equipment, the Developer Tools work on Windows, OS X and Linux so any reasonably new PC will do you fine. If you're thinking about buying an Android phone, you can buy developer phones from Google but those listed on the developer site are quite old now and you'd probably be best off with a Google Nexus One.
Have a look through the Android Developers site:
That will give you the SDK you need, dev guides, sample code, references, resources....all you could want for how to go about developing Android Apps.
Must see that (above 1h video) - http://training.oreilly.com/androidapps/ What more, there is very good book, "Hello Android", where author present how to develop Sudoku :)
I've been reading Pro Android from APress. http://www.amazon.com/gp/product/1430215968?ie=UTF8&tag=ricquablo-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=1430215968
If you're the type of person (like me) who learns from reading code for real apps, you can go through a list of Android apps which are open source, grab some of that code, and try to compile it...