赤ちゃんははいはいができます。
akachan wa haihai ga dekimasu.
When I see this sentence I think it is possible for the baby to crawl.
赤ちゃんははいはいすることができます。
akachan wa haihai suru koto ga dekimasu.
On this one I think the baby has crawled already, so is therefore able.
I would always see people using koto for explaining there hobbies, or something they have done. There are other uses, but in beginner lessons, they keep it simple.
ex.
私の趣味は日本語を勉強することと映画を見ることと漫画を読むことです。
watashi no shumi ha nihongo wo benkyou suru koto to eiga wo miru koto to manga wo yomu koto desu.
I'll try to revisit it later, I am at work, so cant go into too much detail heh..