As a project manager, you can approve timesheets entries made against your projects on the My Projects, Approvals screen. A weekly summary of timesheets by resource and approval status is provided there:

You can:

•    select the weeks you want to approve and click Approve, Unapprove or Disapprove

•    click on the hours in the Approved, Unapproved or Disapproved column to drill into the detailed entries and approve them

•    change the data shown using the filter drop-down list.