Mi amiga me guiñó un ojo desde la otra mesa.

Because me means to me / at me here. With guiñar un ojo, Spanish often uses an indirect object pronoun to show who received the wink.

So:

• Mi amiga guiñó un ojo = My friend winked.
• Mi amiga me guiñó un ojo = My friend winked at me.

In English, we usually say winked at me, but in Spanish the person is often shown with a pronoun like me, te, le, nos, os, les.

That is the normal Spanish expression. Guiñar un ojo is the standard way to say to wink.

It is built like this:

• guiñar = to wink / to squint
• un ojo = an eye

So although it sounds more literal in English, it is completely natural in Spanish. You will hear:

• Me guiñó un ojo. = He/She winked at me.
• Le guiñé un ojo. = I winked at him/her.

Because a wink is done with one eye, not both. So Spanish normally uses the singular:

• guiñar un ojo = to wink

If you said los ojos, it would sound different and would not be the normal expression for winking.

Guiñó is the preterite of guiñar, used for a completed action in the past.

A wink is usually seen as a short, finished action, so the preterite fits very naturally:

• guiñó = winked

This sentence presents the wink as a single event that happened once.

Compare:

• Me guiñó un ojo. = She winked at me.
• Me guiñaba un ojo. = She was winking at me / She used to wink at me.

The imperfect guiñaba would suggest repetition, background description, or an ongoing action.

In Spanish, object pronouns like me, te, lo, la, le, nos usually go before a conjugated verb.

So:

• me guiñó = winked at me

Not:

• guiñó me ❌

This is a basic rule with conjugated verbs:

• Me vio = He/She saw me.
• Te llamó = He/She called you.
• Le sonrió = He/She smiled at him/her.

Here desde means from, in the sense of starting point or location of the action.

• desde la otra mesa = from the other table

It tells us where the wink came from.

Using de would not sound right here for this meaning. Desde is the natural choice when you mean something like:

• from across the room
• from the window
• from the other side
• from that table over there

Examples:

• Me saludó desde la puerta. = He/She greeted me from the doorway.
• Nos miraba desde el coche. = He/She was looking at us from the car.

La otra mesa means the other table: a specific other table that both speaker and listener can identify from the context.

• otra mesa = another table / a different table
• la otra mesa = the other table

So in this sentence, it sounds like there are identifiable tables in the situation, and the speaker means the one that is not this one.

Yes. Amiga is feminine, so it refers to a female friend.

• mi amigo = my male friend
• mi amiga = my female friend

Notice that mi does not change form for masculine or feminine singular nouns:

• mi amigo
• mi amiga

It only changes in the plural:

• mis amigos
• mis amigas

Because mi here is a possessive adjective meaning my, and that form has no accent.

Compare:

• mi amiga = my friend
• mí = me, myself (used after prepositions)

Examples:

• Mi amiga me llamó. = My friend called me.
• Lo hizo por mí. = He/She did it for me.

So in your sentence, mi has no accent because it means my.

Yes. A mí me guiñó un ojo is correct, but it adds emphasis or contrast.

• Me guiñó un ojo. = She winked at me.
• A mí me guiñó un ojo. = She winked at me.

You might use a mí if you want to stress that it was you, perhaps not someone else.

For example:

• No le guiñó un ojo a Juan; a mí me guiñó un ojo.
  = She didn’t wink at Juan; she winked at me.

Guiñar un ojo is a very common and standard way to say to wink in Spain.

You may also hear:

• hacer un guiño = to make a wink / to give a wink

But guiñar un ojo is probably the most straightforward and common expression for learners to know.

For example:

• Me hizo un guiño. = He/She gave me a wink.
• Me guiñó un ojo. = He/She winked at me.

Both are natural, but your sentence uses the very standard verb expression.

Because mesa means table in the furniture sense: a table where people sit, eat, talk, etc.

Tabla usually means board or plank, not a dining table or café table.

So:

• mesa = table
• tabla = board / plank

In your sentence, la otra mesa clearly means another table in the room, probably at a café, restaurant, or similar place.