While my fellow SharePoint MVP John White has written a good article on new-old, one-way, user profile import from Active Directory to SharePoint, it is well worthy to note that the old, FIM based, read&write user profile import is still there.
While there is not many users out there that need two-way communication between AD and SharePoint, there are still some of them. This post is for them. People who do not need two way stuff, are probably better served with the profile import described in John’s post.
So, let’s see how to do the old, FIM based, two way profile sync with 2013 (not much has changed since 2010, you’ll notice).
In Central Administration, open Service management (“Manage Services on server”)
Check if “User Profile Synchronization Service” is running (yes, the one which we know and love). If it isn’t, please start it.
And chose the credentials the service should run under
Go back to Central administration, chose “Manage Service Applications”, and Open the “User Profile Service Application”
Click on “Configure Synchronization Connection”
Add a new connection, if there isn’t one
Fill in the settings for your connection…
… an click on “Populate” button. Chose “Users” checkbox…
And then click “OK”. Go back to User Profile Service Application…
…and click on “Configure Synchronization Timer Job”. Set your sync intervals there…
… and back to the User Profile Service Application to do the initial sync… (click “Start Profile Synchronization”)
As this is the first time we are doing the sync, chose “Full sync”
You will notice that the “Profile Synchronization Status” has changed from “Idle” to “Synchronizing”.
Click on the “Synchronizing” link to get the sync status…
Once the sync is finished, the status changes back to “Idle”, and you have the sync results in the Profiles section.
Go back to User Profile Service Application and click on “Manage User Profiles”.
After doing some querying, you see your imported users there…
…with their properties.
And that would be all for the beginning 
