A cross reference table is just an ordinary table it is just a term used in this context.
If you need a cross reference table depends on whether you have a one to many relationship or a many to many relationship.
table1
id
studioID foreign key to studio(id)
studio
id
studioname
With this type of table setup you have a one to many relationship.
An entity in the first table can only use one studio but one studio can be used by different entities. (A bit bothersome using the term entity, let's call it person henceforth.)
A many to many relationship is where one person can use many studios and one studio can be used by many persons.
In the many to many example, each column in the primary key of the cross reference table is a foreign key to the tables that are part of the relation.
create table user(id int auto_increment ,name varcahr(10), primary key(id))
create table studio(id int auto_increment ,name varcahr(10), primary key(id))
create table studioUsage(userid int references user on delete cascade, studioid int references studio on delete cascade, primary key(userid,studioid))
The Mysql support for foreign keys is very weak. It is only supported if you use INNODB as table handler and features such as cascading deletes, is not supported at all.