Note: The form "se (a alguien) dar bien (algo)" only works with pronouns (me, te, se, nos, os). If you want to you specify a name, you have to place it at the beginning (more common) or at the end (rare) of the sentence, the choice depending on what part of the sentence you want to emphasize:
A Pepe se le dan bien los niños. (Pepe is good with kids.)
Note how I used a "with" there, not an "at". Both "to be good at" and "to be good with" can be expressed in Spanish with "dársele bien algo a alguien."
Some answers state that "ser bueno en/con" is more frequent. I personally disagree, but don't forget there may be regional differences. Either way, both are common and understood everywhere.
However, using "ser bueno en/con" poses a couple of problems. The first one would be choosing the right preposition, and the second one is ambiguity. Consider the first sentence, now using a "ser bueno en/con":
Pepe es bueno con los niños.
This sentence could mean either that Pepe is good with them (whenever he has to spend some time with kids he doesn't know, he gets to get on well with them. Kids consider him a "cool guy". That is, you are describing a skill), or that he is nice to them (he generally doesn't ground them when they misbehave, he treats them with kindness and tolerance. That is, you aren't describing a skill but a treatment). Both definitions overlap to a certain extent, but are different. This is made obvious if the sentence is reworded with a superlative form:
Pepe es demasiado bueno con los niños. Los está malcriando.
This makes sense only if one considers the second meaning (Pepe is too nice with the kids. He is spoiling them.), but not the first one, since one cannot be "too skillful with kids".
This ambiguity doesn't arise with objects because one cannot be "nice" to objects. So if the "algo" is a person, go with "se (pronombre) da/dan bien (algo)". Otherwise, any of the two constructions would work.
Finally, it's not easy to parse this idiom because it's, well, an idiom. In general lines, in "se me da bien el ajedrez" (I'm good at chess) you know:
The subject is "el ajedrez".
The Indirect Object is "me".
The pronoun ("se") has no semantic meaning1. It must agree with the subject, but since the subject is always in third person singular or plural, and the third person pronoun is "se" for both the singlular and plural form, it is invariable.
So you can see the subject/object roles are just the opposite as in English (something like what happens with the verb "gustar"), which makes it tricky for Spanish learners. Therefore, and considering subject-verb agreement, the choice between da/dan depends on what you are good at. Consider:
Se me da bien cocinar tartas. (I'm good at cooking cakes.)
Subject = cocinar tartas (sg); verb: da (sg); Indirect Object: me
Se me dan bien las tartas. (I'm good with cakes.)
Subject = las tartas (pl); verb: dan (pl); Indirect Object: me
Here, the Indirect Object can be reduplicated for emphasis under the form of "a mí/a ti/a vos/a usted/a él/a ella/a nosotros/a vosotros/a ustedes/a ellos", and it can be placed at the beginning, in between, or at the end:
A mí se me dan bien las tartas. (common)
Se me dan bien las tartas a mí. (rare)
Se me dan bien a mí las tartas. (rare)
Se me dan a mí bien las tartas. (almost yoda-sounding)
EDIT: Pondering Ustanak's answer, I got to the conclusion there is indeed a second meaning for this saying. In English, "to be good at/with something" is pretty much a permanent thing: you either are good or not. In Spanish, however, "dársele bien algo a alguien" can describe both a permanent trait or the quality of a performance. An example of the former would be all the sentences provided so far, but now consider the following example:
El primer examen se me dio bien, pero el último se me dio bastante mal.
If you only considered the "trait" meaning, you would get nonsense: "I was good with the first exam, but terrible with the second (?)". A much more sensical translation would be "I did well on the first exam, but did terribly [screw it up] on the second". So "dársele bien algo a alguien" can describe a performance too, and in that sense it would be something temporal (how you did on a given occasion) instead of permanent (how good you are at something). This is in syntony with the general meaning of the saying: if you are good at something, it would be expected be that you do well when doing that thing. Both senses ("to be good at" or "to do well in") are valid, although (at least in Spain) the first one is more common. In Chile, on the other hand, it seems to be a common phrase. Per Ustanak's comment:
Se me dan bien las cosas.
...would mean "things are going well" or "I'm doing well". However, if you want to be understood everywhere, you should try to avoid such expression.
1 The pronoun is standing there because the verb requires it, but has no real meaning in the sentence. Some grammarians call it a "marca de verbo pronominal" (pronominal verb marker), thus saying that the verb is "pronominal" (i.e., it always takes a pronoun), and that the pronoun itself would be the "marker" of such a verb. This concept is key because in Spanish pronominal verbs are just as common as phrasal verbs in English, so it's a good thing that one gets familiar with them.
