clipping/pinning to prevent twisting

This seems like it should be so simple a task, but I'm having a very difficult time with it, and it's frustrating me to no end. I'm just not sure if I'm doing something wrong or what. I recently bought a box of clips instead of pins to see if that would help (tails are STILL twisting on me despite rigorous pinning) and I figure I must be doing something wrong.

So, like. Dumb question but, is there a certain way I need to be pinning everything? Admittedly, I'd still consider myself a person with basic sewing knowledge, so please don't be afraid to point out something that might seem obvious. I guess like I'm wondering, do you have to lay out your pattern flat, or is there a way the seams are supposed to line up or something? I'm at my wits end.

Any tips on how to clip/machine sew work (especially like things with curves such as tails) would be hugely appreciated.

Thanks