In terms of actual entity representation, it would work something like this:
If you have a 1 to 1 relation, then only one of the entities will have a corresponding table, the other will be included in the corresponding record.
Example: 1 Patient has only 1 Hospital Bed, and there can only be 1 Patient in 1 Hospital Bed. In that case, Hospital Bed should be represented by a column (bed number) or a collection of columns in the Patients table.If you have a 1 to Many relationship, then you create a Foreign Key relationship between the first(1) entity (which will be the primary key entity) and the second(M) entity.
Example: 1 Patient can take only 1 Drug, but 1 Drug can be taken by Many Patients. In that case, DrugId would be a foreign key in the Patients table.Finally, in the case of a Many to Many relationship, the typical technique is to create an association table which will contain two foreign keys, one from each entity, and perhaps some other columns.
Example: 1 Doctor can work in Many Hospitals and 1 Hospital employs Many Doctors. Therefore, we should have an association table, say MedicalJobs, which will have foreign keys HospitalId and DoctorId and perhaps Salary, JobId etc.
Concerning your Trial - Patient question, if one trial has many patients but a patient can only participate in one trial, then it is a 1 to many Trial-Patients relationship, therefore, all you need is a foreign key TrialId in the Patients table.
I hope this clears it out. If you need additional explanation, please comment on this post.