Disegno una spirale nel quaderno.

In Italian, subject pronouns (io, tu, lui/lei, etc.) are often omitted because the verb ending already tells you who is doing the action. Here disegno ends in -o, which marks first person singular present indicative (“I draw”). Adding io is not wrong, but it’s redundant:

• (Io) disegno una spirale nel quaderno.

Most native speakers simply say Disegno…

Disegno is the present indicative form of disegnare (to draw). Specifically, it’s first person singular, meaning “I draw” or “I am drawing.”

Conjugation of disegnare in the present indicative:

• io disegno
• tu disegni
• lui/lei disegna
• noi disegniamo
• voi disegnate
• loro disegnano

Una is the indefinite article (a/an) for feminine singular nouns. It’s required here because Italian grammar almost always needs an article before a countable noun. Omitting it would sound odd or change the meaning:

• Disegno spirale nel quaderno. (ungrammatical)
• Disegno la spirale nel quaderno. (“I draw the spiral in the notebook,” referring to a specific one you both know about)

So una spirale = “a spiral,” nonspecific.

Many Italian nouns ending in -e can be either masculine or feminine, and you usually learn the gender with the noun. However, spirale is always feminine. You spot that by noting the article and adjective agreement:

• una spirale lunga (feminine)
• il principio (masculine, another –e word)

When in doubt, check a reliable dictionary.

Nel is the contraction of in + il (in the). You use it because quaderno is a masculine singular noun that takes the definite article il. Thus:

• in + il quaderno → nel quaderno

Without contraction, it would be unidiomatic:

• in il quaderno (wrong)

The preposition in implies “inside” or “within the pages of” the notebook:

• Disegno una spirale nel quaderno. (“I draw a spiral in the notebook,” i.e., on a page inside.)

Su means “on (top of),” more about surface:

• Disegno una spirale sul quaderno. (“I draw a spiral on the notebook,” perhaps on its cover or top page.)

Both are grammatically correct but convey slightly different locations.

Yes. Sul = su + il (“on the”).

• Disegno una spirale sul quaderno.

Difference in nuance:

• nel quaderno: inside, on one of the inner pages.
• sul quaderno: on top of the notebook itself or on its cover.

Context will tell you which preposition is more appropriate.