I am trying to drape a net using the cloth physics, but then is there a good way to make it look like the four corners are pulled and "staked" in a certain place? My first thought was some kind of force field, but then I was curious if I could somehow pin the corners of my net to the plane. Maybe the best way is to just do it manually. I'm very new to Blender so just looking for some direction. Here is an example of the net without the corners being pulled tight to the plane.
Cloth Sewings springs
I would add a sewing edge to each corner of the surface and set its ending point to a pinning group.
From the linked page of the manual:
...Sewing springs are virtual springs that pull vertices in one part of a cloth mesh toward vertices in another part of the cloth mesh.
Extrude the corner vertices and assign the edge and the new vertices to a different vertex group:
Starting from a similar scene where there is a single mesh acting as an obstacle and a grid surface falling from the top by the scene gravity and with cloth physic enabled, you should first of all enable the collision for the cloth:
Notice how the pinned vertex stay still on the ground because Pinning checkbox is was enable. The sewing edes are now simply connecting the vertices the belongs to by freely altering their lenght
You'll probably have to lower the friction parameter too, gradually increase the resolution and quality of the simulation to achieve best results. For example I had to smooth out the top faces of the obstacle in order to lower the friction and transmit tension across the whole surface.
Finish by introducing the Sewing Spring vertex group in the Shrinking to restrict the tension only on the edges if that is the kind of simulation you are aiming to.
Here's what a possible result could look like by using the Shrinking group.
Notice how next to the 3D cursor the cloth is clearly not pulled, while in the previus example there were a bit of tension in that place also.
Pinning with Hooks
Create as many Empties as pinned vertices. They should be in the same place. Create Hooks for those vertices with each Empty. I have done it by selecting Empty in Object Mode than with SHIFT selecting Plane, go to Edit Mode, select vertex and CTRL+V > Hooks > Hook to Selected Object.
Note: For creating net you can utilize this method: How to create and design hoops net and attach ot to a hoop?