Определите время действия в придаточном предложении по отношению к главному: 

 

 

They said that the surgeon had already operated the patient.
одновременность
предшествование
следование
It was noticed that those drugs reduced the risk of reinfection
одновременность
предшествование
следование
The doctor said she had already made an order for the X-ray examination.
следование
одновременность
предшествование
There was no evidence that the disease would spread.
одновременность
предшествование
следование
She said that she wanted to be a dentist.
следование
одновременность
предшествование
We did not know whether the seed had been brought to the fields.
следование
одновременность
предшествование
It was clear that they knew all the facts and were acting accordingly.
одновременность
следование
предшествование
We thought about the mistake that he had made.
предшествование
одновременность
следование
He said that he had been ill.
следование
одновременность
предшествование
She said that her Father was ill.
предшествование
следование
одновременность
The professor said that nobody had come to the lecture.
следование
предшествование
одновременность
He prescribed me the drug that would relieve an acute pain.
одновременность
предшествование
следование
I knew that researchers had found a new virus.
одновременность
следование
предшествование
I knew that researchers had found a new virus.
одновременность
следование
предшествование
He told me that he would not smoke so much.
одновременность
следование
предшествование
He stuck to the belief which had been found wrong.
одновременность
предшествование
следование
learned twenty words which I had found in the text.
одновременность
следование
предшествование
I saw that the girl was very beautiful.
следование
одновременность
предшествование

Короче, одновременность - 1; следование - 2; предшествование - 3They said that the surgeon had already operated the patient - 3It was noticed that those drugs reduced the risk of reinfection - 1The doctor said she had already made an order for the X-ray examination - 3There was no evidence that the disease would spread - 2

She said that she wanted to be a dentist. - 1

We did not know whether the seed had been brought to the fields - 3It was clear that they knew all the facts and were acting accordingly - 1

We thought about the mistake that he had made - 3He said that he had been ill - 3She said that her Father was ill - 1 

The professor said that nobody had come to the lecture - 3

He prescribed me the drug that would relieve an acute pain - 2I knew that researchers had found a new virus - 3

He told me that he would not smoke so much - 2

He stuck to the belief which had been found wrong - 3

... learned twenty words which I had found in the text - 3

 I saw that the girl was very beautiful - 1.

Делается это так: 1 - если глаголы стоят в одном и том же времени (past simple тут, в основном)2 - если придаточная часть содержит would3 - если глагол стоит в past perfect (had found, had come и т.д.), что по сути обозначает предшествование.