I grow spinach in-season and buy big bags off-season. It is important to try to pick the newest/freshest bag at the store, examining the back and bottom for longest shelf life.
Any not used in the first few days (# days depends on how old it is) should be taken out of the bag to dry out some. The texture will be worse but it beats slime (fungus and bacteria). Depending on how many other moisture-losing items you have in your fridge, and how often you open the door (varying the humidity), you could leave it to air-out in the fridge, leave the bag outside the fridge to dry out the inside, then put it back in the bag.
It will need examined daily once it gets closer to a week old (varying conditions as above). When you first start to see dark green edges on leaves, you can either eat the rest, freeze it (good for about 6 mos.), blanch it then freeze it (good for about 18 mos.) or dehydrate it in either a dehydrator or your oven's lowest setting. Don't eat even the slightest darkened wet looking areas without cooking it first, or drenching in vinegar and letting sit for a few minutes. Vinegar kills bacteria and fungus... up to a point, it doesn't remove the bacterial byproducts which can be toxic in large doses.
If you have the spinach stalk, not just the leaves, cut the base end at an angle to expose more, moist tissue. stick it in a tall narrow glass of water enough to cover the cut end and store in the fridge without a bag, like it is a bouquet of flowers in a vase. This is the best way to get longer fridge life for spinach, and most other things but it does take up more valuable fridge shelf space.