[verb (dictionary form)] + ことができる
The structure ことができる expresses the ability or possibility of doing something, equivalent to "can" or "be able to" in English. It is formed by attaching ことができる to the plain (dictionary) form of a verb.
To express inability, conjugate できる into its negative form: できない (casual) or できません (polite).
To talk about past ability or possibility, conjugate できる into the past: できた / できました.
Japanese also has a potential verb form (e.g. はなせる話せる, よめる読める) that expresses the same meaning more concisely. The potential form is more common in everyday conversation, while ことができる tends to appear in written language, formal contexts, and announcements.
Both forms are grammatically correct, but ことができる sounds slightly more formal or explanatory.
When using a noun with できる directly (without こと), the meaning is the same but the structure is different: Noun + ができる. For example, にほんご日本語ができる means "I can (do) Japanese." The ことができる pattern specifically attaches to verb phrases.