How are different circuit form factors (SODIMM, PCIe) designed and manufactured?
They are just PCBs. You can just make them. You should find the standard measurements so that you can make sure your PCB has the right measurements to fit into the slot. Maybe someone has a template file for you, but if not, you can make it yourself from scratch.
The connector style is called an edge connector or card edge connector. Your PCB software should have a footprint for one. It should work as a normal connector, except you don't have to solder any component there because the PCB itself is the connector.
Some manufacturers will be able to dip the edge of the PCB into a gold plating machine - just the edge - so you can get a better connection without having to gold-plate the entire board. They might also be able to bevel the edge of the connector, which makes it easier to insert into the slot, since the part you put into the slot is thinner and then it self-centers as you push it in.

What type of software is used to create these?

Any PCB software.

for example, can you make a SODIMM based PCB on Eagle or KiCAD,

Yes.

or are there special programs?

Maybe - I don't know.

How would one manufacture these?

They are just normal PCBs, except for the edge plating and bevelling, but most PCB manufacturers won't have a problem with that (they might cost extra though!). For your own experiment, I think you can afford to skip these steps, but don't quote me on that.

is it possible to manufacture these form factors in small quantities the was most traditional PCBs are manufactured?

Yes, they're just normal PCBs.

I have designed a single board computer that i would like to make a DIMM style prototype for, any good books you would recommend ?

Buying recommendations are off-topic here