You could invite someone by just suggesting they visit WikiTree.com. Please do this with all your neighbors and friends right now. :-)
If you're inviting a family member it's best if they don't start at the home page. If they do they may not get connected to your family tree.
The best way to invite a family member is to include an e-mail address when you add them to your tree. For example, if you click the link at the top of your Person Page to add your father and include an e-mail address along with his name, he will automatically be sent an invitation.
If you've already created a page for a family member you can add their e-mail address at any time. Click "edit" on their Person Page.
What if your family member lost the invitation?
You can have a new invitation sent by clicking the link the below the E-Mail Address field on their Edit-Person Page.
Changing their e-mail address has the same effect. For example, let's say there was a typo in Moe Schmoe's e-mail address so Moe never got the original invitation from Joe. If Joe fixes the address a new invitation will be sent.
Advanced WikiTreers may be interested in the following.
Our term for someone who has been invited to join WikiTree but hasn't become an active user yet is "Pending Person". This distinguishes them from a "Passive Person" who may be a long-dead ancestor.
Person Pages are essentially all the same but the person can be Passive, Pending, or Active.
Put another way: a person record without an e-mail address is Passive. When you invite someone to join by adding an e-mail address for them their record is considered Pending. When the person accepts the invitation and creates their own password they "take possession" of the person record and it becomes Active.