After tracking hours on a project, you can easily bill them to your client by clicking "Invoice Hours" from the project's Time Tracking page.
This will create a new invoice with your timesheet of unbilled hours on it. If you only want to include hours from a certain date range, you can select the dates upon invoicing.
Once you've created an invoice with your new timesheet, you can also edit the hours you're billing for from the invoice itself.
If you've made a mistake, you can always delete the invoice and choose what to do with the associated hours.
Currently, you can only send timesheets to clients when invoicing them. This process also works for tracking time without an hourly rate. If no hours have an hourly rate, an invoice will still be created with a link to the generated timesheet.