Let's look at how to say "can" in Japanese:
First the 2 ways that use できる dekiru or the -masu form できます dekimasu (they both mean "can do", "able to do")
NOUN + GA + DEKIMASU
日本語ができる。 nihongo ga dekiru. [lit. Japanese can do.] (I) can speak Japanese.
This just says, "Japanese can", but of course what is meant is (I) can speak (or write) Japanese. Usually pronouns are left out when the context is clear. For more on pronoun usage, click here Notice が ga is used with dekiru.
EXAMPLES: できません。 dekimasen. (I) can't do (it) (or できない。 dekinai) スカイ・ダイビングができますか？ sukai- daibingu ga dekimasu ka? Can (you) sky-dive?
SIMPLE VERB + KOTO GA + DEKIMASU
日本語を話すことができる。 nihongo o hanasu koto ga dekiru. [Japanese speaking-thing can do] I can speak Japanese.
To add a verb, you must stick koto ga dekiru to the simple verb. A simple verb usually ends with a 'ru' or a 'su,' and is the shortest form of the verb. X tabemasu (masu form of 'to eat') O taberu (simple form) + koto ga dekiru
X hanashimasu (masu form) O hanasu (simple form) + koto ga dekiru
EXAMPLES: 納豆を食べることができません。 natto o taberu koto ga dekimasen. (I) can't eat natto. (or できない。 dekinai)
トイレに行くことができます。 toire ni iku koto ga dekimasu. (I) can go to the bathroom.
And one that doesn't use dekiru
VERB + ~RARERU or ~ERU
日本語が話せる。 nihongo ga hanaseru. [Japanese can speak] I can speak Japanese
This basically means the same thing, but uses a different way. I won't say much on this now, as I want to concentrate on dekiru. But "can" can be acheived by changing the verb's ending. To learn about verb groupings click here
GROUP 1: ADD ~eru 話す hanasu (to speak) 話せる hanaseru (can speak) 書く kaku (to write) 書ける kakeru (can write)
GROUP 2: add ~rareru ; Most verbs fall into this category 食べる taberu (to eat) 食べられる taberareru (can eat) 見る miru (to see) 見られる mirareru (can see) [You can also say 見える mieru which may be more in use!]
GROUP 3: These are the irregular verbs. These 2 are all you have to worry about 来る kuru (to come) 来られる korareru (can come) [A shorter version 来れる koreru is also in use - Maybe recent Japanese has been working to shorten these long tongue twisters.] * する suru (to do) becomes できる dekiru (as discussed above)
ピーマンを食べられますか？ pi-man o taberaremasu ka? Can you eat green peppers? (It seems a lot of Japanese children hate green peppers) パーティーに来られますか？pa-ti- ni koraremasu ka? Can (you) come to the party?