What are the technical terms/techniques involved in sewing "paper bag" like bags?
So there is a lot to unpack here, hah. But seeing from other comments that you are new to sewing, I can understand how it can be a little daunting to try and make a direct replication of something you've found online.

There is no formal "technique" you will need to follow, but rather a knowledge and understanding of the materials you will need to sew a project. Here is a rough guide to the process I follow when trying to replicate something:


Determining if you want to try and hand sew by hand or a sewing machine. I would go with a machine since this bag looks like it has nothing more than straight stitches.
Material of the bag. There is a lot to consider here - the amount of weight you want the bag to be able to carry, do you want it waterproof, do you want it easily washable? Picking your use for the bag will help determine the type of fabric you will want to use for your project. I would go with a thicker cotton, cotton blend, maybe a thicker flannel if you want to replicate the fuzziness of this particular example. These fabrics are also kind to beginners. An additional item to consider is if you want your sides to be able to stand up like that, you might need what is called "interfacing" and it comes in iron-on or sew-in and it can help add rigidity to the sides and bottom support of your bag. 
Construction layout of the bag. You will want to self-draft a pattern or try to find one on the internet that you can copy and test out measurements on before you start cutting and sewing together. This is as easy as getting some paper or cheap muslin cloth and drawing some shapes and pinning them together to see if you like how it is looking, and determine how you want to assemble the bag.
Taking your pattern/muslin draft and cutting out the real fabric and going through the final assembly. 


Other assorted musings about the provided image:


The zig-zag cut at the top is called "pinking" and there are special scissors that do that called pinking shears. They are typically used to cut fabrics that have a tenancy to fray, and not necessarily used for decoration. 
You'll want an iron to be able to flatten seams (where the fabrics are sewn together) and to create those creases on the sides of the bags. Irons will typically come with heat settings for the types of material you are using.


I hope this can give you a good starting point!