Select a user you want to change permissions for and click on the "..." menu. From there, choose Edit permissions.

First, you need to define if this user is an employee, a client, or a contractor. 

Employees can be assigned one of these five roles:

Staff is a role with a basic set of permissions. Staff members can manage tasks and task lists and collaborate on projects.

Staff members can't access company settings, financial information, or cost rates.

They can't manage People and Companies or see other people's time entries by default.

These two permissions need to be added manually to a Staff member.

Coordinator sits between a Staff member with extended permissions and a Manager. This user has access to everything project-wise, besides project financials (budgets and profitability). You can also choose whether the Coordinator will be able to have unlimited or restricted access meaning he can see all public projects but he can't see private projects he isn't assigned to.

Manager is a role that manages projects/budgets and has access to all deals and budgets as well as their financials.

You can give your employees a manager role, but decide if you want to limit their access only to deals and projects they’re members of.

Managers don't have access to company settings or cost rates.

Can this role add new deals/projects?

Yes, a Manager with restricted access can add new deals and projects.

In addition to all the information, a Manager can see, the Profitability Manager also has access to the budget's profit and revenue information as well as the profit of the whole organization.
Profitability managers can also have unlimited access so they can access all deals and projects or their access can be restricted so they only see deals and projects they are assigned on.

Admins can manage everything, including cost rates and general organization-level settings.

Clients can manage tasks and task lists and collaborate on projects. Clients can also get access to budgets and timesheets.

This is a global permission setting for a specific client. To give a client access to a specific budget, you need to go into the Project, select the Budget and turn Client access on from the sidebar located in the upper right corner shown in the picture (below).

💡 In the Essential pricing plan, Clients can only see projects, regardless of their permission level. In the Professional pricing plan, Clients with access to budgets can also see budgets and time entries.

Contractors can't get any special permissions, they can only collaborate on Projects, and manage tasks and task lists:

💡 For more information on permissions by role, please check out the following article:
Productive - Permissions by role.