Tables and layouts are two different things. In filemaker you build relationships between tables not layouts. However, each layout is based on a table, so the relationships that link each table will in turn help control how the data from each table is displayed on your layouts.
First thing you'll want to read about in the help files are "Portals". Portals give you a window that allows you to list data fron a different table that is related to the current record. Thus, you can set up a layout based on your patient table and then add a portal that lists related visit records. The help file will take you step by step through this process, so try that and then post any questions/problems back here and we'll see what we can do to help.
Second thing you'll need to do is to create a relationship linking your two tables that allows you to use the relationship to create records in the Visits table.
Open File | Manage | Database | Relationship
If you haven't already done so, click and drag to create a relationship linking the Patients::ID to Visits::ID.
Double click this relationship line and select the check box labeled "Allow creation of records in this table via this relationship" for the Visit table.
Now you can create a portal that displays Vist records for a given patient and when you start entering data in the bottom blank line of the portal, the Visits::ID field will automatically get the Patients::ID number of the current record.