Deck stairs pulling apart and railing wobbly
Hard to tell whether you have screws or nails holding everything together right now. It is either nails - which can, relatively easily, come apart, or screws which can come apart but not as easily.

If you have nails then I would reinforce using some long (e.g., 3") screws and you should be set. I would want two screws into the end of each tread. The railing is sometimes a bit trickier, but screws to supplement the existing nails is a good start. If that doesn't take care of all the wobbling of the railing then you may need to replace parts or add some additional supports. Of course, if you find any cracked or rotted pieces, or if anything cracks when you drive in screws, then you need to replace those pieces.

If you already have screws then I'd be a bit more concerned as that may be a sign of the wood rotting (and therefore not holding the screws any more) or that there is just too much movement of the ground causing everything to come apart.