- First make sure, you have permission to open site in SharePoint designer 2010.
To check this go to SharePoint 2010 central administration website then go to general application settings then click SharePoint designer. Select the web application that is hosting your site collection and make sure SharePoint Designer is enabled.
2. Second thing is client integration should be enable for your web application, which is hosting your site collection.To enable client integration follow these steps.
- Go to central administration> security then click specify authentication provider;
- Select web application which is hosting you site collection which you want to edit using SharePoint designer 2010 and click 'Default' below the 'Zone'
- Select the select 'Yes' radio button in the Client Integration section and hit the Save button.
- Close your SharePoint Designer 2010, if it is already open and try to open your desired SharePoint 2010 site.