Learn Hardcore Japanese: watasi ha nihongo ga wakaru you ni natta.

は marks the topic "as for me," while が marks the grammatical subject inside the clause.
In this sentence, the inner clause is 日本語が分かる. The subject of 分かる is 日本語 (the thing understood). 私 is only the topic of the whole sentence. So we get 私は [日本語が分かる] ようになった.

Why 日本語が, not 日本語を?

Because 分かる takes が for the thing that is understood. It’s a mental-state verb (like 見える, 聞こえる) that typically marks the stimulus with が. 日本語を分かる is nonstandard in Tokyo Japanese; you may hear を in some dialects or certain fixed expressions, but stick with が.

What does ようになる mean?

Pattern: verb (plain) + ようになる.
Meaning: a change resulting in a new ability/habit/state, "to come to (be able to) do ~."
Positive: 分かるようになる = come to understand
Negative: 分からないようになる or more commonly 分からなくなる = come to not understand (anymore)

Why is there に after よう?

よう is a noun meaning “manner/state” (from 様). With なる (“become”), nouns take に: become into X. So (V) ようになる literally means “become into a state such that (V).”

Is there a difference between 分かるようになった and 分かってきた?

分かるようになった: arrival at a new ability/state; the change is completed (often implies “and now I can”).
分かってきた: the understanding has been increasing; emphasizes the ongoing, gradual process (“it’s been making sense”).

How would I make this sentence polite?

Change the final verb to polite past: 私は日本語が分かるようになりました. The verb before ように stays in plain form.

Do I need to say 私?

No. Japanese often omits obvious topics. 日本語が分かるようになった will usually be understood as “I” from context.

Who is the grammatical subject of 分かる here?

日本語. With verbs like 分かる, the experiencer (“me”) is usually the topic (私は) or can be marked for emphasis as には: 私には日本語が分かる (“Japanese is understandable to me”).

Can I say 日本語を分かるようになった?

Avoid it. Standard usage is 日本語が分かるようになった. を分かる appears in some dialects and in a few expressions (e.g., 気持ちを分かる), but learners should default to が.

Does なった mean the change happened in the past but might not hold now?

By default it implies a completed change with a present result (“I’ve come to understand [and I do now]”). To talk about a past change that no longer holds, add context: 昔は日本語が分かるようになったが、今は忘れた.

Why is は pronounced “wa” here?

When は is the topic particle, it’s pronounced “wa.” As part of a word (like はな), it’s “ha.” This is a historical spelling convention.

How is ようになる different from ようにする?

ようになる: non-volitional result/state change (“It became so that ~ / I came to be able to ~”).
ようにする: deliberate effort (“make sure to ~ / try to ~”). Example: 日本語が分かるようにする = work to make it so I can understand Japanese.

When do I use plain なる without よう?

Use (noun/na-adjective) + になる and (i-adjective) + くなる:

上手になる (become skillful)
きれいになる (become clean/pretty)
早くなる (become fast) With verbs, use V + ようになる.

Is there a difference between 日本語が分かる and 日本語ができる?

Yes:

日本語が分かる: you can understand/comprehend Japanese when hearing/reading.
日本語ができる: you can use/speak Japanese (general ability). For speaking specifically: 日本語が話せる.

Can I replace 日本語が with 日本語は?

Yes, to topicalize or contrast: 日本語は分かるようになった (“As for Japanese, I’ve come to understand it [maybe unlike other languages]”). が is neutral/new information; は adds topic/contrast.

Is it okay to write わかる in kana instead of 分かる?

Yes. わかる in kana is very common. If you use kanji, 分かる is standard; 解る/判る exist but feel specialized or old-fashioned.

How do I say “I became unable to understand Japanese”?

Most natural: 日本語が分からなくなった.
Also possible: 日本語が分からないようになった, but 〜なくなる is the usual pattern for loss of ability/habit.

Where can adverbs like “gradually” or “finally” go?

Place them before the clause or before なった:

だんだん日本語が分かるようになった
やっと日本語が分かるようになった
もう日本語が分かるようになった

Can I use this pattern to talk about other abilities?

Yes. Examples:

泳げるようになった (I became able to swim)
早起きするようになった (I started getting up early)
辛いものが食べられるようになった (I’ve become able to eat spicy food)

Is ように here the same ように as in requests like 分かるように説明してください?

Same word, different construction:

Your sentence: V + ように + なる = change of state.
Requests/purpose: (someone) が V + ように = “so that (someone) can V.” Example: 日本語が分かるように説明してください (Please explain so I can understand).