In the client detail, click "Add membership":
Here you can choose the membership and the price you want to give this client. This way, you can also give the membership for free.
Note: Only a one-time membership can be assigned this way. A recurring membership can't be assigned from the admin panel — it needs the client's payment card and a payment confirmed by their bank, so the client has to buy it themselves on your public page. Once they have, you can manage it from the admin panel as usual: pause it, resume it, or cancel it.