You can set up access privileges in Manage | Security that limit a user's access to specific records. See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set this up.
Open File Options from the File menu. There's an option there that specifies what account name and password is used to log in to the file automatically. Either clear this check box or specify an account name that has a defined password and leave the password box empty.
Thank you for answer to part 2. Got that "fixed" :)
Was reading through the "Editing record access privileges" and I do not know how to set up what I am wanting to do.
I go under the Privilege Set Name and under Records and choose Custom Privileges. Under Table Name, Clients, I want the View to be limited to only clients for that trainer. I have a table Clients with _pkClientID, which are records for that clients and _fkTrainerID which is the the Trainers table that that client is under.
You'll need to come up with a way that uses the user's Account Name to match specific records by account name. If you added a text field and entered the account name of the trainer into this field, then:
AccountNameField = Get ( AccountName )
could be used to control access to specific records in the table.
You could also add an account name field to the Related Trainers table and then you could use:
Get ( AccountName ) = Trainers::AccountNameField
to control access to records in the Clients table.
And once you have that working, there are some fairly straightforward ways to keep records covered with the "no access" screen from appearing in a user's found set.
That worked! How do I get the records with "no access" from appearing? :)
I used your second option: Get ( AccountName ) = Trainers::AccountNameField
Any find performed by the user or a script will automatically omit the no access records from the found set produced by the find. You can create a script that performs a find either when the file is opened or when the layout is entered that performs a find patterned after this example:
Enter Find Mode
Set Field [YourTable;:SomeFieldThatAlwaysHasData ; "*" ]
Perform Find 
Ok so I have it set up this way and it is not working:
I set this up on File Options, Script Triggers, On Window Open with this script:Specify target field - Clients::_pkClientIDCalculated result - Clients::Firstname
Enter Find Mode
Set Field [Clients::_pkClientID;:Clients::Firstname]
Perform Find 
When you have "YourTable" in the set field which table am I suppose to put in there and which field? Client or Trainer table? I assume the "SomeFieldThatAlwaysHasData" would be a field in Client table correct?
Figured out what I did wrong! Thank you for your help! :)