The People Picker is the control you see on the page when a column or field needs to contain a user. (Not just the text representing a user’s name, which you should really almost never do, but the actual user object as understood by SharePoint.)
It looks something like this. (This is an example from the Add Users page for Site Permissions.)
At this point, when they see the ‘No exact match was found.’ message, most people move on to option 2.
There’s a third way which can be quicker. You can just type a part of the user’s name in the box and hit enter or the Check Names icon, as in option 1) above. When you get the ‘No exact match was found.’ message, click on the name which has been underlined with the squiggly red line.
While there was no exact match found, there were matches, you’ll see them, and you can select the one you want.
Keep in mind that the more specific you can be in what you type the better the results will be, much like you are used to in your email client, whether it is Outlook, Gmail, Lotus Notes, or whatever.