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I want to make a custom face (or what you call it, sorry I'm new to this)
For example I have a plane cube like this:
And I want to make a small face out of it, so I can have separate texturing to it (If you have suggestions on how I can do it on a smarter way, please do tell me, for now, this is the best idea I have)
I want to have something like this. Thank you in advance!
There are many tools used for mesh modeling that you can use, the simplest to get you started is probably the knife tool.
In edit mode press K and then click where you want to corners of the new face (also called a polygon) then press ⏎ Enter to confirm the cut or Esc to cancel. During the cut you can press C to help keep your lines straight.
Some other tools used for modeling are the loop cut and subdivide to split a face into multiple faces. You can also add single vertices and make a face from 3 or more unconnected vertices, it is easy to find beginner tutorials on mesh modeling.
Note that simply cutting a face into another will leave you with an n-gon, which is a face with more than four sides (compared to tri or quad faces). While n-gons can be helpful during the modeling process, as you progress you will find times when they can cause issues. It is always recommended to maintain a quad based mesh as much as you can. In your example that would mean adding at least another two edges.
