Different ways to deploy a web-application designed and implemented in vs2013 on sharepoint online

Hi,

I have the following:

I have sharpoint 2010 on cloud(i.e. Office 365). I have designed a web application and I want to deploy that to the sharepoint

What are the approaches or the ways I can do that. 

Please listout them or share some resources.

Note: I do not have sharepoint installed on my machine. The web-application will read and update the data on sharepoint.