• The woman who lives next door is a doctor. (or The woman that lives ... )
  The woman lives next door.     who (= the woman) is the subject
• Where is the cheese that was in the fridge? (or the cheese which was ... )
  The cheese was in the fridge.     that (= the cheese) is the subject

You must use who/that/which when it is the subject of the relative clause. So you cannot say
'The woman lives next door is a doctor' or 'Where is the cheese was in the fridge?'.

• The woman who I wanted to see was away on holiday.
  I wanted to see the woman.
  who (= the woman) is the object
  I is the subject
• Have you found the keys that you lost?
  You lost the keys.
  that ( = the keys) is the object
  you is the subject.

• The woman I wanted to see was away. or The woman who I wanted to see ...
• Have you found the keys you lost? or ... the keys that you lost?
• The dress Lisa bought doesn't fit her very well. or The dress that Lisa bought ...
• Is there anything I can do? or ... anything that I can do?

Note the position of prepositions (in/to/for etc.) in relative clauses:

Tom is talking to a woman - do you know her?
→ Do you know the woman (who/that) Tom is talking to ?

I slept in a bed last night - it wasn't very comfortable
→ The bed (that/which) I slept in last night wasn't very comfortable.

• Are these the books you were looking for? or ... the books that/which you were ...
• The woman he fell in love with left him after a month. or The woman who/that he ...
• The man I was sitting next to on the plane talked all the time. or The man who/that I was sitting next to ...