The ESB Studio requires a new installation. You need to export your 6.1.x projects from your local 6.1.x workspace and import the project with the ESB Studio 6.2.x. If you use a shared (remote) Project you need to upgrade Talend Administration Center first, and then connect to your remote project without further actions required.
Studio projects can be used without any manual migration. When the Data Services, Jobs and Routes are opened in the ESB Studio, the components that need changes will be upgraded automatically.