Texturing pulled meshes

I don’t know if i can phrase this in a way that is legible to others; but ive been creating models for a long time using sketchup, and the process of adding textures for more complex models with higher polygon counts has always perplexed me.

Let’s say that I draw, with line tool, and 6 sided shape. I then copy the shape and paste the lines in a scaled down version of the shape inside itself. Then, I use the push/pull too the raise the shape in the middle. I then draw lines to connect both shapes into one.

This usually does not present an issue when apply a texture to the entirety to the model. But, if pull one of the faces or scale the model in a way that is not a direct reflection (aka adding faces) then texturing becomes a pain. When I paste a texture, it just onto this object afterwards the texture is all over the place.

Are my methods just not very good and should i try something else? Is there any way to fix this issue? I know people created more complex models with textures that work fine. I would just be very interested to know how.

(You should upload an image for such an visial question!)
Make sure that you apply textures to the faces directly and not to the group/component from outside.