There are three ways to put someone in a company: invite them by email from the company's page, set the company on their account, or let your single sign-on do it. A person can be in one company at a time.
Inviting people
Open the company's page: in your dashboard, Discussions › Manage Companies, then click the company's name. Members of the company can open it too, with Manage company on their profile.
Click Invite a new person, enter one or more email addresses (separated by commas) and, if you like, a message, then click Send invite.
Each person gets an email with a link. Someone new creates their account from it; someone who already has an account logs in. Either way they join the company. Until then, their invitation is listed under Pending invitations on the company's page.
Adding someone who already has an account
Open their page (click their name anywhere in the dashboard), click Edit this user, choose the company under Company, and click Save changes. They get an email saying they've been added to the company.
To add many people at once, open Account & Settings › Users, tick them, and choose the company from the Set company menu.
With single sign-on
If your customers log in through single sign-on, your site can put them in a company: send company_name in the Multipass token (a company with that name is created if there isn't one), or company_id for a company that exists. An empty company_name (or a company_id of 0) takes them out of their company. See Share your own site's authentication with Tender.
Removing someone
On the company's page, click Remove beside the person. They keep their account, and the discussions they started or follow, but no longer see the rest of the company's discussions.