English has a lot of pronouns. ASL has fewer signs and a system for using them, and once you see the system, pronouns stop being a vocabulary list and become something you can do with a point.
The core idea: pronouns in ASL are pointing. Point at yourself for I or ME. Point at the person you are talking to for YOU. Point at a spot off to the side for HE, SHE, HIM, HER, IT. The sign does not change for subject versus object, and it does not change for gender. The English word changes; the sign does not.
I and me are one sign
I is an index finger touching your chest. That one sign is I and ME. There is no separate "me" sign in everyday ASL; some signing systems invented one for teaching English, but it is not ASL. You is a point at the other person.
He, she, him, her, they
He is a point to the side, and it covers he, she, him, her, and it. Gender is not marked in the pronoun; if it matters, you establish who you mean first, usually by fingerspelling the name or signing MAN or WOMAN, and then point to that spot.
They is the same point swept in an arc, covering a group. We is an index finger that touches one side of your chest and arcs to the other side.
Possessives use a flat hand
Possessives swap the pointing finger for a flat, open palm. My is a flat hand on the chest. Your is a flat palm pushed toward the other person. His is the same flat palm pushed toward the side spot, and it covers his, her, hers, and its. Our arcs a bent hand across the chest; Their sweeps a flat palm across the group.
The rule is clean: index finger for the pronoun, flat hand for the possessive. I versus MY, YOU versus YOUR, HE versus HIS.
Myself and yourself
The reflexives use a thumbs-up handshape. Myself taps a thumb on the chest; Yourself pushes it toward the other person.
Pronouns in sentences
ASL often leaves pronouns off when they are obvious, and often repeats the subject pronoun at the end of a sentence for emphasis. "I'm hungry" can be I HUNGRY, or just HUNGRY with a nod, or I HUNGRY I when you really mean it. All three are grammatical.
Eye gaze does a lot of the pronoun work too. Looking at the spot you set for someone while you sign is enough to mean "he" or "she" in fast conversation.
Practice
Set up two people in space: fingerspell MOM, point right; fingerspell DAD, point left. Then sign: MOM HAPPY, point right. DAD TIRED, point left. THEY (arc across both) HOME. Do it until the pointing feels like talking. It is.
Next: use the pronouns inside question words, and add feelings so you have something to say about yourself.