方: turning an action into a noun for its method
Add 方 to a verb's ます-stem and track the particle changes that come with a noun phrase.
Remove ます and add 方
For a method, 方 is read かた and attaches to the part of a verb left after removing ます. 書きます becomes 書き方, and 使います becomes 使い方: a way of writing and a way of using something.
食べます becomes 食べ方, and 読みます becomes 読み方. Attaching 方 to the whole dictionary form, as in 食べる方, produces a different structure from the method noun discussed here, so checking the ます-form first is useful.
Connect the object with の
漢字を覚える is a verb phrase meaning to memorize kanji; 漢字の覚え方 is a noun phrase meaning a way to memorize kanji. Because 覚え方 is now a noun, the object 漢字 is connected with の in this example.
申込書の書き方を係の人に聞いた。 means that the speaker asked the attendant how to fill out the application form. The entire noun phrase containing 書き方 is the object of 聞いた, so を follows that phrase.
Knowing a method is not performing the action
この機械の使い方が分かりません。 means that the speaker does not know how to use this machine. It neither says that the speaker does not use it nor concludes that the machine is broken.
With expressions containing する, such as 勉強する, a method can be expressed as 勉強の仕方. 方 points to a procedure or manner; whether someone actually studied, or did so successfully, must be established elsewhere in the sentence.
How do you turn 漢字を覚える into a noun phrase meaning a way to memorize kanji?
Show the answer and why
Use 漢字の覚え方. Remove ます from 覚えます and add 方 to make 覚え方; within this noun phrase, connect the object 漢字 with の.