I've lived in many a rented house and although being furnished is a great help, you can never be sure what's "clean" or not. Every time I move into a new place, the first thing I do is give the mattress a good clean with this method and gives me a sweet-smelling bed for the future.
Step 1: What you will need
Cleaning a mattress is very simple and remarkably effective considering the items used. What you will need are:
The mattress that you want cleaned
Some Bicarbonate of Soda (available in all supermarkets in the baking aisle)
A sieve (an icing sugar shaker/duster is even better)
A vacuum cleaner
That is all you need.