This short video showing you how to develop and deploy SharePoint Visual Web Part to Office 365 SharePoint. You cannot develop the Visual Web Part directly to Office 365 SharePoint. You need to develop your Visual Web Part against your SharePoint 2013 on premise then deploy it to Office 365 SharePoint.
Despite Visual Web Part and SandBoxed will continue in the next version of SharePoint. This is one of the features most of the developers are using and one of the easiest ways to customer Custom List and Document Libraries.
The audio inside this video is not great but the video itself will be enough to complete the journey with you.