As @Nickoli already suggested, the question is too broad. Seems you have just started using Tridion so I would like to give a high level answer. You can take that as starting point and go through the documentation and then ask only specific question.

**Can I read content using Tridion Content delivery API in ASP.net Application from my local machine and debug:** 

> Yes, you can. you will be able to debug the asp.net application
> however you wont be able to debug the content delivery calls.

**The process used by content delivery api to read the content is as follows:**

> 1. In your application you will have to store tridion configs and one of the config is cd_storage_conf.xml which has details of which broker
> database to connect.
> 2. Also, while retrieving data content delivery dlls will internally invoke the license check. So you must have valid license.

**How we used to develop ASP.NET and MVC applications before we have DD4T?** 

DD4T has two parts: Publishing and presentation: 

Publishing is set of TBBs which are used to transform the content in formatted xml / json. After content is published, on read presentation portion of DD4T helps you convert xml / json into the models which MVC application can consume easily. Before DD4T, you will have two options: 

> 1. Write dreamweaver tbbs or something similar that will generate html on publish so you will have html pages readily available on delivery. (you can use this option in lieu of DD4T also.)
> 2. If you need MVC based implementation the you will have to implement your own version of functionality that will format the data that can
> be easily converted to models. Since, DD4T is available, you can
> directly use it.