I want to make chest and hip bones like the ones used in rigify. (See image below for more clarification) I've searched several places but couldn't find any information on how to make them. How can I make these for my own armature? Specifically, what types of bones/ constraints do I need to use? 
*Rigify is too confusing for me and I want to make the rig myself for those asking.
Those bones are part of the torso rig, which for a couple of reasons is one of the most complex parts of a bipedal rig. They are control bones that are colocated and both parented to the torso:
by convention the chest is the larger of the two bones. The upper part of the torso is parented indirectly to the chest while the lower part is parented indirectly to the hips. If you enable the Torso tweak bones you can see that this is a pretty complex structure:
A complete description of how to do this would amount to a tutorial on rigging, and that's frowned on by Stack Exchange. You might find Episode 3 - Spine and Torso Rig - Blender Complete Professional Rigging workflow for animations to be a good starting point.
To give you some idea of how complex this is, I've revised some notes from a course I took. Here's the section on the torso:
torso rig - part 1
* Torso rather than spine because it includes the hips but not the neck
* Start with a simple FK rig.
* Use a minimum of 3 bones
* Pelvis
* Rib cage
* Spine connecting them
* He thinks 2 for the rib cage is usually good for humanoid characters
* Quadrupeds, for example, have long spines and will need more spine bones
* Not a good rig because it requires a lot of counter animation
* The rib cage and pelvis rotate independently a lot
* The pelvis pivot point is too low. When people walk, their hips tend to swing from higher up, closer to the waist
* One solution
* Unparent the spine from the pelvis
* Flip the pelvis with an ALT-F
* Constrain the spine to it with a copy rotation constraint
* Problem: animator has to control all four bones. It would be nice to only have to control the top and bottom and have the middle bones follow nicely
* Create a head and neck style rig
* Add the parent bones
* Align them properly
* Set up the child/parent hierarch
* Create the two control bones
* Add copy rotation constraints
* Adjust the constraint influences to create a nice bend
* Problem: real people can swing their hips and chest side-to-side and front-to-back
* Add a new 'middle' control
* Remove the constraints from the middle spine parents
* Constrain the upper parent to the upper and middle control
* Constrain the lower parent to the lower and middle control
* Adjust influences for that nice curve
* Give the middle control a parent and constrain it to the upper and lower controls. This way the animator can normally ignore the middle control but has it when needed
* This rig will do for a lot of characters, but this character has to do acrobatics. The pivot point should be closer to the neck for this.
* It's very hard to move the pivot point. Move the torso instead
* Two bad things about moving the pivot point.
* The translation doesn't show up in the normal transform values
* Earlier parts of the animation affect later parts
These are custom bones, you just need to create a mesh that has the shape you want, them select the bone in Pose mode, go into the Bone properties panel > Viewport Display > Custom Shape and select the mesh as Custom Object:
The bone is no longer a octahedral, it has taken the shape of your mesh, you can now hide the mesh:
Then select the mesh
