Is fixing these stairs as simple as just replacing the stairs and supports?
If the cleats supporting the steps are solid and haven't deteriorated, use 3 inch course-thread screws to re-secure them to the stair stringers (the long outer sections that span from the bottom to the landing. 

If you are in doubt as to the condition of the cleats replace them. I'd use any 2 x stock cut a bit longer than the width of the step. Install it so the cleat's edge is recessed back from the step's edge. From the looks of your foggy photo it appears your steps are 2 x ? stock. If they are in need of replacement (and can't be repaired) replace with similar dimensioned wood. 

Also you might want to consider if there are several steps and/or cleats to be replaced is to install a third stringer between the existing ones. They can be found sometimes pre cut. And it isn't that hard to cut one from a length of 2 x 10 or 12 Douglas fir.