"How did you spend your last/previous week" is already correct. Alternatively, you can also ask "how was last week? / How were you last week?"

'Previous' is not the same as 'last'. I realise that you're studying indirect speech at the moment, so maybe that's where you've got the word from. 'Previous' refers to a time before another time in the past, for example in indirect speech: 'I bought it last week' He said that he had bought it the previous week. This means 'during the week previous to the one when he made this statement'. If you mean the week before this present one, then you say 'last week'. You don't say 'your last week' though. If you talk about a person's last week, it means their final week ie the one before they died! You simply say 'How did you spend last week?' or - more commonly 'What did you do last week?'

You could simply ask "What did you do last week?". This would be a more common way of asking how someone spent their time the week before.