Welcome to working with SharePoint -- you'll find certain things much easier (no need to re-invent things like authentication and backup) but other things will be very frustrating (why can't I just easily add some custom code here to do x...)
Your question is quite vague, but I think what you might be looking for is creating a solution in Visual Studio that you can deploy as a packaged set of files to your SharePoint installation.
I would really highly recommend doing a short class on SharePoint, it should be just what you need to get up to speed since you're already familiar with ASP.NET -- I actually like the videos by Christopher Harrison and Chris Johnson on Microsoft Virtual Academy: http://www.microsoftvirtualacademy.com/training-courses/developing-microsoft-sharepoint-server-2013-core-solutions-jump-start
The videos can be a bit labored because they jump back and forth between a remote dev machine and the local desktops they're using for presentations, but I think that level and speed of content coverage will be perfect considering your previous experience. There is also a course on advanced solutions (Christopher Harrison and Tom Resing) which I found quite helpful.
I also see you listed apps as one of your tags, and I would just throw in a word of advice that SharePoint Apps are fairly different than typical ASP or Server Side development and you might need to do some homework before you begin any serious work – but the videos outlined above cover the App model in a good deal of detail as well.
-Hope that helps!