First, if you enable "allow creation of record via this relationship" for your Vehicles table in the relationship on Manage | Database | relationships that links your two tables, you can place a portal to vehicles on your customer layout and you will be able to enter new vehicle data in the bottom blank row and filemaker will automatically create the new vehicle record and enter the customerID for you.
If you want to enter the vehicle information on the vehicle layout, you'll need to select or enter a customer number. This can be done by formatting the customer ID field with a drop down that lists both customer ID's and their names.
Second, you'll need to script the move from the customer layout to the vehicle layout if you only want to see the records in the vehicle layout that are related to the current customer record. You can do this with either Go To Related record or by setting your script up to perform a find.
Using a Find:
Set Variable [$CustID ; value: Customer::CustomerID]
Go To Layout [Vehicles ( Vehicles ) ]
Enter Find Mode //clear the pause checkbox
Set Field [Vehicles::CustomerID ; $CustID ]
Set Error Capture [on] //keeps no records match.. dialog from interrupting your script if no records were found
Attach this script to a button placed on your customer layout.
Go To Related records can do all of the above in one step. It has many parameters that you can choose for different results and it can be hazardous to your data if you have steps that modify or delete data/records after you do the Go To Related Records unless you implement it correctly. If you want to try Go To Related Records, look it up in the help system (filemaker 11) or see this link: Why Record ID's should not be used as Primary Keys in Filemaker Relationships.