I used to do something similar in a factory.
First of all you need to make a former. You can do this with wood and body filler if you need something exact and smooth. Or for something the rough shape you can use a piece of wood. A cloth over the top will help prevent scratching.
Warm the acrylic on a baking sheet in a hot oven, you will need to experiment with temperature. You can get it to go very floppy indeed. Using gloves, it gets hot, place the heated acrylic sheet over the former, and rub the sheet so that it take on the shape of the former. Keep pressing down until it begins to cool and go rigid again. This is only takes a few minutes for thin materials acrylic.
This works well for simple curves. It even works for compound curves, if the second curve is very slight.
This also works well with Lexan.