What you have there
The names of those are Cam Fittings, Furniture connectors or Flat pack connectors or variations of those phrases. These are a favorite amongst economical furniture suppliers (IKEA is a good example) as it enables the consumer to build it themselves.
These are typically used for joining wood at a 90 degrees. While they are not the strongest join they are great for easy reassembly.
It's also worth mentioning that they are used not just in MDF but particle board as well. If I had to guess that is what is actually under that veneer.
I found a simple video that explains using specific hardware but the logic is the same. I don't think it is possible to provide detailed measurement based instructions since I do not know the dimensions of your hardware but the basics are you need to make 3 holes.
Warning: Ignore the measurements on the pictures below. Those were designed for specific hardware and might not match what you have purchased. Those shots were included for clarity and nothing more.
The larger hole, in the picture below, is where the screw will be eventually placed. The smaller hole is where the bolt will slide through.
The connecting piece will be where the bolt is fastened to. This will pair up with the smaller hole in the picture above. The white piece is an expander that would go into this hole and helps hold the bolt in place
This next picture show the two blocks "assembled" together.
All images were taken from the House of Hacks video linked above
In general, you want all of the holes to be perfect 90 degree angles. Using a drill press would be an obvious tool but space might not allow you that luxury. The suggestions from How do I ensure my drill is perfectly vertical before cutting a hole in my desk? would be a good resource to consider.
There is strength in numbers so it is best to have several along the length of the join. I have not found a good reference for how many. I should think at least 1 every 3 feet with a minimum of one on each end (Speculation). Using some dowels a spacers will help stop lateral movement and are and easy addition. If you do use dowels remember to only glue one end ( if any ) to allow for dis-assembly.
Matching the holes is important but you are allowed some margin for error as the bolt will assemble to the nut at a slight angle.
At this time I do not know the significance of the white part. Possibly a guide for the bolt. Will have to research.