Learn Hardcore Japanese: watasi ha nihongo ga dekiru.

私 means “I” or “me” (the first-person pronoun). In Japanese you often drop pronouns if the context is clear, but here 私 is included to explicitly state the topic (“as for me”) or to clarify who has the ability.

Why are there two particles, は and が, in this sentence?

は marks the topic — it attaches to 私, giving “as for me.”
が marks the subject of できる, which is 日本語 (“Japanese”). When you use verbs of ability like できる, the thing you can do is marked with が instead of を.

What exactly does できる mean in this context?

できる literally means “to be able to do” or “to be possible.” With a noun like 日本語, it expresses ability or proficiency: “I am able to do Japanese,” i.e. “I can use/speak/understand Japanese.”

Why not use a verb like 話す (“to speak”) in the potential form?

You could say 日本語を話せる (“can speak Japanese”), but the more common, broader expression for language proficiency is 日本語ができる. It covers speaking, listening, reading, and writing, not just speaking.

Why is 日本語 followed by が instead of を?

When you express ability with できる (or the potential form of a verb), the thing you’re able to do takes が. So it’s 日本語ができる, not 日本語をできる.

How would you make this sentence polite?

Change できる (plain form) to できます (polite form):
私は日本語ができます。

How do you ask “Can you speak Japanese?” based on this sentence?

Use the polite form plus か to form a question:
日本語ができますか？
In casual speech you might say: 日本語ができる？

Can you replace 私 with other pronouns, and does it change the nuance?

Yes. For example:
– 僕は日本語ができる (casual, softer, male speaker)
– 俺は日本語ができる (very casual, rougher, male speaker)
Women usually stick with 私, though in casual settings some may use あたし. Pronoun choice affects formality and gender impression.