ができる details

ができる

can do; be good at — an ability named as a noun; also, of a thing, that it comes into being or gets finished

兄あには運転うんてんができるけど、私わたしはまだなんだ。

ani wa unten ga dekiru kedo, watashi wa mada nan da.

My brother can drive, but I still can't. casual

駅前えきまえに新あたらしいパン屋やができたよ。

ekimae ni atarashii pan'ya ga dekita yo.

A new bakery has opened in front of the station. casual

Examples

can do; be good at — an ability, skill or subject named by a noun

兄あには運転うんてんができるけど、私わたしはまだなんだ。

ani wa unten ga dekiru kedo, watashi wa mada nan da.

My brother can drive, but I still can't. casual

妹いもうとは英語えいごとスペイン語ごができます。

imouto wa eigo to supeingo ga dekimasu.

My little sister can speak English and Spanish. neutral

彼かれは本当ほんとうに仕事しごとができる人ひとです。

kare wa hontou ni shigoto ga dekiru hito desu.

He is genuinely good at his job. neutral

日本語にほんごができる方かたを探さがしております。

nihongo ga dekiru kata o sagashite orimasu.

We are looking for someone who can speak Japanese. formal

comes into being; gets finished — something new appears, or a task reaches completion

駅前えきまえに新あたらしいパン屋やができたよ。

ekimae ni atarashii pan'ya ga dekita yo.

A new bakery has opened in front of the station. casual

日本にほんに来きてから、友ともだちがたくさんできました。

nihon ni kite kara, tomodachi ga takusan dekimashita.

I've made a lot of friends since coming to Japan. neutral

ご準備じゅんびができましたら、お知しらせください。

go junbi ga dekimashitara, o shirase kudasai.

Please let us know once you are ready. formal

What you can do takes が, never を — ×日本語にほんごをできる — and the topic
particle displaces it under contrast: 英語えいごはできますが、フランス語ごは…

ことができる
The same ability with the host one step apart — ができる needs it named as a noun (運転うんてんができる), ことができる takes the verb clause and reaches every verb (立たつことができる, no noun to name it with); with a する-noun both are open, and the bare noun frame is the spoken default while ことができる is the shape notices and contracts print.
られる（可能）
できる is する's own potential, so 料理りょうりができる and 料理りょうりが作つくれる split the claim — できる names the skill in general, the one-word potential names this particular act being possible today (今日きょうは作つくれない says nothing about whether you can cook).