Show the board you want to share so it is the one on screen, then press Share beside the board's name at the top. (Share is greyed out when several boards are on screen — show one board first.)
The share screen first says What you are sharing: the board and every calendar on it, by name. It lists the people on this board and anyone already invited.
To share with someone who has Helm: type their Helm account's email under Share with. The line below says what they will get. Press Share (the button carries the board's name). Everyone on a shared board can do everything on it. The board stays in your account — only that board is shared, never your whole account.
If they do not have Helm yet: after you type their address, Helm says they don't have Helm yet and offers Invite with their address. They get an email from you asking them to join Helm free, and they land on this board. The screen shows how many invitations you have left and when the invitation ends; you can Withdraw it until they accept. Press Not now to skip. If invitations are not open for your account, the screen says so and nothing is sent.
On the same screen you can Remove a person from the board. Press Done to close it.