Spotting is essential when youre trying to get stronger. Adding weight to bar and lifting it has as much to with physical strength as it does with mental fortitude. If you dont THINK you can lift it, it doesnt really matter how strong you are (but obviously if you arent strong enough it doesnt matter what you think you can do). But more often than not it's someone brain that holds them back from a PR.
So, use a spotter when attempting to lift heavy weights. Although, I dont recommend ever doing singles unless you are competitive power lifter training for a meet. Anyway, having a spotter that knows what he is doing, meaning knows what it feels like to apply enough assistance is key. A spotter will allow you to hold (or support, in the case of a squat) weight that you havent experienced before. That alone will get the brain ready for the lift.
When it comes to adding weight to the bar you dont need a textbook to tell you what to do. If you squatted 315 for 5 last week and are happy with that and want to add more, you should absolutely use a spotter for 325 or 320, whatever. If you only get 3 reps clean then need help for the second 2, it's not a failure. But you shouldnt add weight again until you are able to squat the weight by yourself, even if your spotter is close by. If it takes more than a couple of weeks you should reevauluate your nutrition. And of course, your spotter should be doing as little work as possible to keep the bar moving in the right direction. Obviously the bar will slow down as you get closer to your max but you never want the bar to stop or EVER move in the opposite direction before the spotter adds some help.