Learn Turkish: Hemşire nabzımı ölçtü ve doktoru beklememi söyledi. - The nurse measured my pulse and told me to wait for the doctor.

This is how we form indirect commands in Turkish. To say 'told me to wait', you literally say 'told my waiting'. We take the verb stem bekle-, add the short verbal noun ending -me, then the possessive -m (my), and finally the accusative case -i because it is the direct object of the main verb söyledi.

How do we know who the nurse told to wait if there is no word for 'me' before söyledi?

The possessive suffix on the verbal noun tells us who is supposed to do the action. In beklememi, the -m means 'my waiting'. If the nurse had told us to wait, it would be beklememizi söyledi (told our waiting).

In English we wait 'for' the doctor. Why is it doktoru instead of doktor için?

In Turkish, the verb beklemek (to wait) takes a direct object, not a postposition like 'for'. You directly 'wait someone'. Since 'the doctor' is specific in this context, it gets the accusative case ending -u.

I know the word for pulse is nabız. Why did it become nabzımı here?