Okay - without having access to your instance, I can't put the actual objects/field names in, but here's an example where any Opportunity (Object A) where type = 'Existing Customer - Upgrade', we'll create a new Contact (Object B) where Lastname = Opportunity Name, and Contact Title = Opportunity StageName.

So obviously not a real life example, but I think you can easily adapt it to do what you want...note that unlike with buttons, the fields names for both source and target have to be the API field names...

Best practice for triggers is to write a simple trigger, and then pass off handling to class...so first we have the class, and that class also contains a test script...

public with sharing class ManageOpportunities {

public static void afterInsert(Opportunity [] optys) {
//Put all new records in a list so we only execute one DML statement
List<Contact> newcons = new List<Contact> ();
 
//Loop through records passed in by trigger
   for (Opportunity o: optys) {
     //only create for correct type
         if (o.type.equals('Existing Customer - Upgrade')) {
//we can create a contact based on Opty data and add directly to a list
             newcons.add(new Contact (LastName = o.Name, Title = o.StageName, Languages__c = o.Account_Number__c));
         }
    
    }
    //once loop is finished, check if any new records were requried
    if (newcons.size() > 0) {
//if so create       
 try {
        insert newcons;
        }
    //error handling depends on your use case...but as a simple example, this won't stop Opportunities being created
    //and debug log will say why insert of contacts failed
       catch (Exception Ex) {
        system.debug (ex);
        }
    }
    
} //end after insert

static testmethod void  testafterinsert() {
//Create new Opportunity that WILL create a new contact
Opportunity testo = new Opportunity (Name = 'testconcreated', CloseDate = system.today(), StageName = 'Prospecting', Type = 'Existing Customer - Upgrade');
insert testo;
//Check new contact created and data updated correctly
Contact testcon = [Select Id, LastName, Title from Contact where LastName = :testo.name];
system.assertequals(testo.StageName, testcon.Title);

//Create Opportunity that WON'T
Opportunity testonocon = new Opportunity (Name = 'testconnotcreated', CloseDate = system.today(), StageName = 'Prospecting', Type = 'Existing Customer - New');
insert testonocon ;
//Check no new Contact created...
system.assertequals(0, [Select count() from Contact where LastName = :testonocon.name]);


}

} //end class

And then the trigger to call that class

trigger ManageOpportunities on Opportunity (before insert, after insert) { 

    if(Trigger.isInsert && Trigger.isAfter){
        ManageOpportunities.afterInsert(Trigger.New); 
    }  
} //end trigger

That should get you started...