We can use the verbs 「する」 and 「なる」 in conjunction with the 「に」 particle to make various useful expressions. We are used to using the object particle with 「する」 because something is usually done to something else. We will see how the meaning changes when we change the particle to 「に」. As for 「なる」, it is always used with the 「に」 particle because "becoming" is not an action done to something else but rather a target of change. The only grammatical point of interest here is using 「なる」 with i-adjectives and verbs.
As already explained, using 「なる」 with nouns and na-adjectives presents nothing new and acts pretty much the way you'd expect.
For adjectives, using the verb 「する」 with the 「に」 particle is just a review back to the lesson on adverbs. However, for nouns, when you use the verb 「する」 with the 「に」 particle, it means that you are going to do things toward something. This changes the meaning of 「する」 to mean, "to decide on [X]". This is a common expression to use, for instance, when you are ordering items on a menu.
If you think this expression is strange, think about the English expression, "I'll go with the hamburger." Exactly where are you going with the hamburger?
Because the 「に」 particle is a target particle that is used for nouns and by extension na-adjectives, we need to use something else to show that something is becoming an i-adjective. Since "becoming" expresses a change in state, it makes sense to describe this process using an adverb. In fact, you'll notice that we were already using adverbs (of a sort) in the previous section by using 「に」 with na-adjectives.
You may be wondering how to use 「なる」 and 「する」 with verbs since there's no way to directly modify a verb with another verb. The simple solution is to add a generic noun such as a generic event: こと （事） or an appearance/manner: よう （様）. These nouns don't refer to anything specific and are used to describe something else. In this case, they allow us to describe verbs in the same manner as nouns. Here are some examples of how to use these generic nouns with 「する」 and 「なる」.
You can modify a verb with 「なる」 or 「する」 by first making it into a noun clause and then treating it just like a regular noun. Pretty clever, huh? I hope the literal translations give you a sense of why the example sentences mean what they do. For instance, in the fourth example, 「～ようにする」 translates into "to make an effort toward..." but in Japanese, it's really only a target towards acting in a certain manner.
Since potential verbs describe a state of feasibility rather than an action (remember, that's why the 「を」 particle couldn't be used), it is often used in conjunction with 「～ようになる」 to describe a change in manner to a state of feasibility. Let's take this opportunity to get some potential conjugation practice in.