Let's say a PC attempts to punch herself. Can she do so?

• If the PC is willing and deliberate, can she miss?


• Does she make an attack roll? If so, what AC is she trying to hit?


• How much damage would it cause?

I was considering how this would work in general, but it would also be relevant if the PC was under a charm spell, or maybe she wanted to do it for social influence (like intimidation).

The PC can try anything

Let's get back to basics. The game flow goes like this.

Case 1: the DM assesses that the outcome is not in doubt.

1. The DM describes the environment.
   
   The DM describes the PC being in (for example) a room, or a cave, or standing in the village square.


2. The players describe what they want to do.
   I want to punch myself


3. The DM narrates the results of the adventurers’ actions.
   You punch yourself.
   
   Player then asks: how much damage do I roll for?
   
   DM asks: Were you trying to harm yourself?
   
   Player answers: Yes.
   
   DM says either:
   You successfully did (1+STR modifier) damage to yourself or
   Not your day, you didn't do any damage to yourself

We note in Chapter 7 that the DM should not call for a roll unless the outcome is in doubt. While that is aimed at ability checks, it can be applied here as well, so ...

Case 2: the DM sees that the outcome is in doubt; a die roll is called for.

1. The DM describes the environment.
   
   The DM describes the PC being in (for example) a room, or a cave, or standing in the village square.


2. The players describe what they want to do.
   I want to punch myself
   
   2a. DM calls for a die roll: roll a d20 versus your armor class, with advantage {or with disadvantage} On a hit, do 1 + STR modifier damage to yourself; on a miss not your day, you tried to punch yourself and missed {hilarity ensues}
   
   2b. Player roll turns out as a 15 + mods, and scores a hit, and has a strength of 16.


3. 
   

   The DM narrates the results of the adventurers’ actions.
   You punch yourself. It hurts quite a bit, you take 4 points of damage.

   
   
   

   A DM can apply circumstantial advantage or disadvantage to any situation where it seems appropriate. This DM would. @NautArch points out that it is kind of hard to hit yourself IRL, so it may be more "realistic" to apply disadvantage rather than advantage.

   
   

The result of a hit may be zero damage, though

With a Strength score of 9 or less, there is a -1 modifier to the attack, and 1-1 = 0. This was confirmed in the 2019 Sage Advice Compendium, page 11.

Can damage be reduced to 0 by resistance or another form of damage reduction? There is no damage minimum in the rules, so it is
possible to deal 0 damage with an attack, a spell, or another effect.

Yes, you can attack yourself

You are simply a target and you'd run through your normal attack action, including rolling your D20 against your AC (STR mod + Proficiency) and applying your unarmed strike damage(STR mod +1).

Whether or not it's at Advantage/Disadvantage would be up to the DM if they felt it was reasonable to apply.

Why go through it all?

Because making an attack is never a guarantee. You can try and hurt yourself, but you may not be successful. That's normal. The roll against your AC covers the factors involved (your armor, your desire to actual connect against yourself, your own toughness, the awkwardness of trying to strike yourself, etc.) and running through the exercise of rolling allows those factors to play a role in determining the outcome.