ことができる・ ができるcan; be able to
できる is "can": what someone is able to do, or what is possible somewhere. A skill goes before it as a noun. Any other action goes in as a verb with こと.
possible here
At this store, you can pay by card.
With a noun
Noun + が + できる
The noun is a skill or an activity: a language, a sport, cooking, driving.
With a verb
Verb dictionary form + こと + が + できる
泳ぐ → 泳ぐことができる. It has to be こと, not の.
Polite, negative, past
できます・できない・できた
"Can't" is できない. "Was able to" is できた.
A skill: Noun + ができる
English needs a verb here: "can speak", "can ski", "can drive". Japanese only needs the noun, and it takes が, not を.
I can speak a little Japanese.
Mr. Tanaka cannot drive.
No, not at all.
An action: Verb + ことができる
The action is said as it normally would be, particles and all, and ことができる goes on the end.
You can rent a bicycle at the station.
At this library, you can use the internet for free.
When I was a child, I couldn't ride a bicycle.
This long form is at home in explanations, notices, websites and writing, where it says what a place, a ticket or a service lets you do. In conversation people mostly build "can" into the verb instead: 読める, 行ける. There ことができる is correct but a little stiff.
Where English "can" is something else
"Can you…?" as a request is てください, and "can I…?" asking someone's permission is てもいいですか. できますか asks only whether it can be done.
Sounds odd: 窓を
Are you able to open the window?
The request is 窓を開けてください.
And 分かる already has "can" in it. "I can understand" is just 分かります.
Not said: 日本語を
(I can understand Japanese.)
日本語が分かります.
できる is also "is made" and "is ready"
With no "can" in it at all, できる says that something has come into being or is finished.
A new hotel has been built in front of the station.
Dinner is ready.
I've made a Japanese friend.
Close neighbours
"Can" built into the verb, with the same meaning.
My younger sister can speak English.
Check yourself
1Which particle?
兄は
Choose an answer to see why.
2"I can swim a hundred meters."
百メートル
Choose an answer to see why.
3Which sentence is right?
Choose an answer to see why.
More detail
こともできる
が gives way to も for "can also". Shops and guides say it constantly.
You can also pay by card.
運転できる
A noun that takes する can also join できる directly: 運転できる, 予約できる.
More sentences
My younger sister can swim.
You can use this room until six p.m.