There are so many things that can help this... that it's almost impossible to teach you why it's happening unless you actually understand nCloth.
Basically though I'll give you a quick pipeline of how I go about making nCloth:
Go into nucleus, Scale Attributes -> Scene scale. This has dramatic effects, so try to stick with 1, 0.100, 0,010 kind of values, and set it to the one that works best with a default nCloth (make a new nCloth and disable your current one if you have to figure it out!).
Go into the nClothShape node now and change the colliion flags and self collision flags AND their respective Thickness and Self Collide thickness while keeping a close eye on (by toggling) Solver Display Collision Thickness, Self Collision Thickness, and Off constantly.
Finally, change max iterations to a low value. Something like 50, 500, 1000. The deafult 10,000 is too high for most things you want to be doing with ncloth. This saves a lot of time.
Finally, save your scene while it's working, and especially before changing any value more than 1. Before even simulating (if you have read and not just jumped into playing by now) change the playback looping to once and set it to 500 and when you feel comfortable, move it down to 50 for further experimentation. Changing some nCloth values to more than 1 make the cloth bog down the entire program sometimes, and it's actually faster to quit maya and reopen it (as tedious as that is).
As a side note, you may want to create a new project for yourself to test various nCloth settings. It is definitely a pain in the ass to learn when it bugs out all the time, so setting the bend solver to Simple may be a good idea, so you can at least hold ESC to cancel the sim if the sim starts glitching up. I would especially stay away from Rigidity and Deform resistance myself, but it depends on what you're doing.
From the screenshot you've provided it looks like you may want to add a new edge so that it bends perfectly at that specific location. Although you CAN get results with just a quaded sheet, it will then give you the problem of having a kind of "lump" before flowing over the edge of the object without edges there. To further that effect, you can actually make an area around that specific location that you want to crease a little better once you smooth it (both these images use that).
You can actually also go back to, specifically, the scene scale and raise it by 0.05's until you're satisfied with how fast it falls. Use some of the default maya examples (then go into their Max Iterations and turn them way down, as well as quickly setting the Thickness and Self Collide Widths to logical values) just to see whether or not your main nCloth was working correctly. The last thing that may make a huge difference is just chaning the friction and stickiness values. Having something like 0.9 frictions, 0.1 stickniness will really help set a cloth onto something so that its form stays in a wrinkled way that looks nice without popping or sliding off of your collision object(s).
Definitely one of the most frustrating but worthwhile tools to learn though, for sure. I was going to write more, but a lot of questions can be answered by searching online.