You can set a billable method and rate for your project in the 'Billing' section of the project overview:

There are three types of rates available:

By selecting a user-based rate, the billable amount will be calculated from the billable rate of each user. You can set their default billable rate on their profile in the Users tab.
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The billable rate set on their profile will be used as a default on all projects. You can override the default billable rate with a custom billable rate project by project in the 'Members' tab of the project overview:

If you bill time spent on different tasks at different rates, choose a task-based rate. You can then enter a different hourly rate for each task on the project's task list, like this:

Select this option if all time logs on your project will be billed at the same hourly rate, regardless of the task or the user performing it. Every hour tracked on this project will be billed by the rate that you enter here:

If you select this option, the billable amount will not be calculated from your time logs and all time logs recorded on the project will be marked as non-billable.

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If you need a simple hourly rate for yourself, select the user-based rate, and enter your billable rate in the Users tab (explained above).

If you are not creating invoices with My Hours, the best way to track the fixed fees is by adding a budget to your project.

In My Hours, the billable amount for invoices is always calculated from the recorded time and hourly rates. If you need to create an invoice for a fixed fee, there is a workaround available. In this case, please select the Project- based rate as a billable method and set the rate at $0.00 per hour. Then you can add the fixed fee amount as an expense to just one of the recorded time logs in the invoicing period. This way you can invoice the flat amount to your client.

If you bill some tasks on a project at an hourly rate and others with a fixed fee, please select a Task-based rate. Set the hourly rate for the flat fee tasks at $0.00. Then add the fixed fee amount as the expense to just one of the recorded time logs on the flat fee task in the invoicing period.

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Please check this article to learn how to change the rates for new time logs only and keep the old rate for existing time logs.