Learn Hardcore Ukrainian: Я хочу позичити ручку.

borrow: позичити щось у когось (literally, borrow something from someone) — Я хочу позичити ручку у вас.
lend: позичити комусь щось (lend someone something) — Я хочу позичити вам ручку. In your sentence, with no recipient mentioned, listeners usually understand it as borrow.

Why is it ручку and not ручка?

Because it’s the direct object in the accusative case. Ручка is a feminine noun; its accusative singular is ручку (e.g., бачу ручку, I see a pen).

What’s the difference between позичити and позичати?

Aspect:

позичити = perfective, a single, completed borrowing (one time).
позичати = imperfective, a process or repeated/habitual action. So Я хочу позичити ручку = I want to borrow a pen (once), while Я хочу позичати ручки would mean something like I want to be borrowing pens (as a habit), which is unusual in this context.

Is Я necessary? Can I just say Хочу позичити ручку?

Yes, you can drop Я. Ukrainian often omits subject pronouns when the verb ending makes the subject clear. Хочу позичити ручку is natural.

Is Я хочу... a polite way to ask?

On its own, it sounds more like a statement of desire. For polite requests, use:

Можна ручку? (Very common and friendly: May I have/borrow a pen?)
Чи можна позичити у вас ручку? (Could I borrow a pen from you?)
Позичте, будь ласка, мені ручку. (Lend me a pen, please.)
Softer desire: Я хотів би/хотіла б позичити ручку. (I would like to borrow a pen.)

How do I show who I’m borrowing from?

Add у + person (genitive): Я хочу позичити ручку у вас / у Марії / у колеги. Word order is flexible: Я хочу позичити у вас ручку / Я хочу у вас позичити ручку are both fine.

Should it be у вас or в вас?

Use whichever sounds smoother (euphony rule). Here у вас flows more naturally than в вас. In practice, у вас is the standard choice in this phrase.

If I want to say I want to lend (not borrow) a pen, how do I say that?

Use the dative for the recipient:

Я хочу позичити вам ручку. (I want to lend you a pen.)
Я хочу позичити комусь ручку. (I want to lend someone a pen.)

Can I use взяти instead of позичити?

Взяти means to take; it doesn’t itself imply you will return the item. To sound like borrowing, add context:

Можна взяти вашу ручку на хвилинку? (May I take your pen for a moment?) For clear borrow/return intent, позичити is safest.

Are there articles like a/the? How do I express a pen?

Ukrainian has no articles. Ручку can mean a pen in general. If you need to specify, you can say одну ручку (one pen) or якусь ручку (some pen).

Does ручка always mean pen?

No. Ручка can also mean a handle (door handle) or a little hand (child’s hand). In everyday contexts with verbs like позичити, it normally means a pen. If needed, specify type: кулькова ручка (ballpoint pen), гелева ручка (gel pen), пір’їнна ручка (fountain pen).

How do I make this even more polite?

Add будь ласка and/or use a conditional:

Чи не могли б ви позичити мені ручку, будь ласка?
Будь ласка, можна у вас позичити ручку? You can place будь ласка at the start, middle, or end without changing meaning.

What pronouns/cases go with borrow vs lend?

Borrow: позичити щось у когось → object in accusative, source in genitive after у. Example: позичити ручку у Марії.
Lend: позичити комусь щось → recipient in dative, object in accusative. Example: позичити Марії ручку / позичити їй ручку.

How do I pronounce it naturally?

х in хочу is like the sound in Scottish loch.
ч is like ch in church.
у is like oo in food.
и is a short i sound (closer to ih). Stress: хо́чу, ру́чку. Vowels are not reduced as in Russian, so о stays clearly о.

How do I say I don’t want to borrow a pen?

Add не: Я не хочу позичати ручку (general/habitual) or Я не хочу позичити ручку (one time).

How do I say I wanted to borrow a pen?

Use past tense with gender:

Masculine: Я хотів позичити ручку.
Feminine: Я хотіла позичити ручку.