benkyou no houhou wo dankaigoto ni kaemasu.

A natural reading is:

べんきょう の ほうほう を だんかいごと に かえます。

Word by word:

• 勉強 = べんきょう
• 方法 = ほうほう
• 段階 = だんかい
• 変えます = かえます

So the full sentence is:

べんきょう の ほうほう を だんかいごと に かえます。

の connects two nouns.

• 勉強 = study / studying
• 方法 = method / way

So 勉強の方法 literally means the method of studying or study method.

Here, 勉強 modifies 方法. In English, we often put the first noun directly before the second noun, but in Japanese this relationship is often shown with の.

Similar patterns:

• 日本語の先生 = Japanese teacher / teacher of Japanese
• 料理の本 = cookbook / book about cooking

を marks the direct object of the verb.

The verb here is 変えます, which means change something.
What is being changed? 勉強の方法.

So:

• 勉強の方法を変えます = change the study method

This tells you that 方法 is the thing receiving the action of changing.

段階 means stage, step, or phase.
ごと means each or every, in the sense of dividing something into units.
With に, it becomes an adverbial expression.

So 段階ごとに means:

• at each stage
• for each stage
• depending on the stage

The idea is that the method is not the same all the time; it changes from one stage to another.

In this sentence, 段階ごとに functions like an adverbial phrase, describing how or according to what division the method changes.

The に helps turn 段階ごと into a phrase meaning:

• for each stage
• stage by stage

You will often see ごとに after nouns:

• 一日ごとに = every day / day by day
• 人ごとに = for each person
• 国ごとに = by country / depending on the country

So 段階ごとに fits this same pattern.

This is a very common question, because 変える and 変わる are a transitive/intransitive pair.

• 変える = to change something
• 変わる = something changes

In this sentence, someone is actively changing the study method, so Japanese uses the transitive verb 変えます.

Compare:

• 勉強の方法を変えます。
  = I change the study method.

• 勉強の方法が変わります。
  = The study method changes.

So the version in your sentence focuses on a person intentionally making the change.

Japanese often leaves out the subject when it is clear from context.

So this sentence could mean:

• I change the study method at each stage
• We change the study method at each stage
• You should change the study method at each stage
• One changes the study method at each stage

The exact subject depends on the situation. This is very normal in Japanese.

変えます is the polite non-past form.

Japanese non-past can express:

• a present habit
• a future action
• a general rule

So depending on context, this could mean:

• I change my study method at each stage
• I will change my study method at each stage
• You change the study method according to each stage

Japanese does not force the same present/future distinction that English does.

The basic order is natural, but Japanese word order is more flexible than English as long as the particles stay correct.

This sentence:

勉強の方法を段階ごとに変えます。

could also be written as:

段階ごとに勉強の方法を変えます。

Both are natural. The difference is mostly emphasis or flow.

• 勉強の方法を first: focus first on what is changed
• 段階ごとに first: focus first on when/by what division it changes

Sometimes learners expect a noun compound here, but 勉強の方法 is the more straightforward and natural expression for method of studying.

You may also see:

• 勉強法 = study method / study technique

That is a very common and compact word.

So these are all possible, but with slightly different feel:

• 勉強の方法 = neutral, explanatory
• 勉強法 = concise, common as a set term
• 勉強方法 = less natural than the other two in many contexts

They are similar, but not exactly identical.

• 段階ごとに = at each stage / stage by stage
• 段階に応じて = according to the stage / depending on the stage

段階ごとに emphasizes division into separate stages.
段階に応じて emphasizes adjusting in response to the stage.

In this sentence, either could make sense, but 段階ごとに has a nice each stage separately feeling.

It breaks down like this:

• 勉強の方法 = study method
• を = object marker
• 段階ごとに = at each stage / depending on the stage
• 変えます = change

So the structure is:

[object] + を + [adverbial phrase] + [verb]

More literally:

[the method of studying] [object marker] [for each stage] [change]

This is a very standard Japanese sentence pattern.