My company has SharePoint server farm setup and run on internet and local. Now we have to develop some application on it. How can we do that from VS2010 on PC/Laptop (which
You can develop SharePoint applications without SP installed but will be limited to using the REST Api, ClientContext API or an external connector like Camelot .NET Connector for SharePoint from Bendsoft.
Generally SharePoint developers work in a virtual environment with SharePoint foundation installed creating their deployment packages locally.
Here is a good starting point if you want to set a virtual environment up for development. http://msdn.microsoft.com/en-us/library/ee554869(office.14).aspx