Learning to draw

Pencils: ...10H, 9H...H are hard. HB is in the middle, and those which are with the letter B are soft. 10H is very hard. It scratches the paper, hence, I have never used it in my life. hard pencils are used for light shading. Soft pencils are used for shadow shading. Sounds strange, but yes. light also should be shaded. any place without shading cannot be left on the paper. Exceptions: highlights. THis is not light. This is the brightest places on the object which you are drawing. they can be the most close places to the source of light or if a subject is glossy, then these are something like reflections on the part which is not in a shadow.

When I draw I always use pencils 4h, 2h, HB, 2b, 6B. Soft pencils are used for making dark places which cannot be made by hard pencils. The darkest places should be different kinds of holes, but never whole shadows.

By the way, I should mention about paper too. Paper for drawing should be quite thick and lets say, the opposite for the paper for watercolors-smooth, but not glossy.
one more important thing is that forget about using your fingers to spread pencil around your work. Normally people use for this purpose napkins or other things, but it is better not to use finger, because you might like to do it. I use my fingers only when the shading is too harsh, when I want kinda soften it. I have never use those erasers which you have, but I know how to use them, because I saw. They are mentioned to make details, like fur, hair, brows etc. but you can substitute it by the standard eraser.

now about erasers: use the one which form 'sousages' when you erase. they collect pencil from your work and do not smudge it on the paper.

In drawing it is better to start with easy shapes. When I started, on my first year we were drawing different kinds of shapes like squares, pyramids, spheres...they were on the table and our task was to draw their construction, another words, not only what is visible but also what is not visible. we didn't focus on shadings those times. The important thing was to understand how the shapes were formed, because on the second year figures because more complicated and on the third and fourth year we started to draw faces of people. faces contain all those forms which we were drawing all these years, so it became easier to understand what is the shape of the lips, eyes, cheeks - make construction which helped to understand how light is falling on the face.

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pencils: you don't have to buy a lot of pencils. it is not necessary. if only you fell uncomfortable about them. Hard pencils are light. try to draw with 4h pencil on the paper with all your force. the line will be quite dark but still light grey. And try the same with the pencil 4b (or some other from B category if you don't have). you will see that the line is almost black. it means that if you will use a hard pencil for the light, the light on your drawing will never become too dark (it is not supposed to be dark). In past all students in my school were drawing even with 2b pencils, but their drawings were light. they were afraid to use force.  Me too.  But what is important: don' t be afraid to show your confidence about drawing, use all color of the pencil. The most important thing: choose right pencils. so, very hard pencils for the light. I use even 2H gor the shadow, because i use force and 2H for the light is too dark. but it depends. all you need is to try and understand what is more comfortable for you.

about paper - you are right. use it under your hand, because otherwise your drawing will be smudged. and don't worry about the kneaded eraser. use your normal eraser. with time your works will become more sophisticated, so you will need something very small to erase, but right now don't focus on it. paper that you use is ok.

Now about shapes. we were drawing them to practice. but as far as you don't have any white gypsum shapes (most probably), you can read about this in Internet. And study how the light is going on the square or spherical shapes. I think that you should have the idea how it should look like.

so, here you have shapes to study (i will send you more later. those will be mine):
[link]

and here different kinds of shading;
[link]
I prefer cross hatching. it is more classical. lines are not supposed to be straight. cross hatching is used for different purposes. to show the shape also (when you are shading a sphere you need to show that it is round). for sketch you can use different kinds of shading, actually what is easier for you. but cross hatching looks nice and professional, but it comes with time. all you need to learn now is light and shadows.