A billing rate is what you charge a client for one hour of someone's time.
Default rate for a person
Go to Team, open the ⋯ menu next to the person, and choose Change role, manager or access. Enter their Billing rate (per hour).
Admins and Finance can also set a Cost rate: what an hour of that person costs you. It's used for project profit and is never shown to clients or managers.
A different rate on one project
Open the project, go to the About tab and use Billing rates on this project. A rate here beats the person's default rate on this project only.
A project billed in another currency (for example USD for an overseas client) needs a project rate for each person. Default rates are in your home currency.
When rates apply
Rates are fixed when time is approved. Changing a rate affects time approved from then on, not work that's already approved or invoiced.
If time shows no rate when you create an invoice, set the rate, then ask the manager to return and re-approve that week.