Jtdylktuy

I can make sense of

Me gusta (a mi) - it gives me pleasure.

However, the expression

Se me da bien -- I'm good at it

doesn't make sense to me due to the presense of "se". If it was "me da bien", I'd understand it. With "se" it seems that "I(!) give to it ..."

Why "se"?

How does the expression translate literaly?

It's the pronomial verb form (often called reflexive, which is apparently a subtype of pronomial) darse.

Literally, you could translate "(esto) se me da bien (a mi)" as It *gives itself* to me well.

You could literally translate "Se me da bien" as "it Blooms to me"

the expresion indicates that you are good doing it; that you can get it to it's best in a easy way.

(Sorry for bad english)

Se me da(to me),se les da (them)etc... is always referred to the capability of someone of doing some activity. That "se" is there just to make the verb reflexive (Darse bien/mal)

You have choosen a tricky one there. It's a complex verb and a complex structure.

According to the D.R.A.E

dar

22. tr. Hacer sufrir un golpe o daño. Dar un bofetón, un tiro. U. t. c. intr. Dar DE bofetones, DE palos.

...

49. prnl. Dicho de una cosa: Suceder, existir, determinar.
Se da el caso. En circunstancias dadas.

In

Se me da bien

we've got the 49 meaning. prnl indicates that it's a pronominal verb

The grammatical term "pronominal" means "relating to a pronoun," so
pronominal verbs require a reflexive pronoun. They’re often
incorrectly referred to as reflexive verbs, when in fact the latter
are just one type of pronominal verb. The defining characteristic of
pronominal verbs is that their subjects are acting upon themselves.
Pronominal verbs are much more common in Spanish than in English.

What sets pronominal verbs apart from non-pronominal verbs is that
pronominals must be conjugated with a reflexive pronoun, which
always agrees with the subject. {source}

As noted in this text - originally in Spanish -

se - Es un morfema al servicio exclusivo de la significación del
verbo; forma parte del verbo - verbo pronominal - y juntamente con él
constituye el núcleo del predicado. Su supresión es imposible o cambia
el significado del verbo.

[English] se - It's a morpheme exclusively related to the verb
meaning; it's a part of the verb - verbo pronominal - and them both
form the nucleus of the predicate. It's removal is not possible
because it may change the meaning of the verb.

As stated above, if you have just

Me da bien

then you got a different meaning. Probably 22 [see D.R.A.E above] in its intr [intransitive] meaning because there is no object in that phrase, it's not the usual "dar/give" meaning because nothing is being given explicitly. That sentence lacks information, it's not complete for a native speaker. I tend to fill it in my head as Me da bien [para el pelo], an idiom.

The most accurate translation of: I'm good at it

in Spanish is: (Yo) soy bueno en ello

Notice that it's practically a word-by-word translation. It seems that you're trying to compare "I'm good at it" with "Se me da bien", two completely different phrases. They've got practically the same meaning but they are constructed differently. In the Spanish version the subject is it, the thing that I master, and that subject is omitted while the subject in the English version is I and the pronoun it is present as a complement.

Let's reorder the phrase: (Ello) dáseme bien

where

(Ello) - it - subject omitted

dáse - verb

me (a mí) - to me

bien - well

This reordered version is percieved as archaic, it's more or less how Spanish were spoken centurys ago but you can see that all the elements are present in your original version.
I've not found an idiomatic version in English, it should be something like it's my forte (suggested by Mv Log in the English Learners Site)

it - subject

is - verb

my - particle that establish the relation with me

forte - positive characteristic

Hope all this text helps you to understand the sentence.