In case the client does not want to give you Business Manager access as Admin, here are some other things you can do.
If your client has a Business Manager account but you don't:
You can do the same process in Step 1 but instead of Admin access, your client can select "Employee access" but your client would need to select all the assets you will have access to as you will no longer be able to do it as shown in step 3.
If you have a Business Manager but your client doesn't:
You'll need to request for advertiser access for both the page and the ad account.
You will ask your client for his/her Ad Account ID and FB Page url.
Once you have it, follow the instructions below.
If neither of you has Business Manager accounts:
Your client will need to add you manually. Refer to the guide below: