つくる　（作る）is "to make" while します　(verb form する）is to do. I think there is a different phrase for "making friends" because 作る　is literally making or creating things.

Please remember that sometimes the literal translations don't make sense because our languages are very different. In this case, remembering the meaning of the sentences would be better. For example, before you make friends, "I want American friends / I want to have American friends / I want to make friends with American people / I want to become friends with American people", we say: アメリカじんと友達になりたいです / アメリカ人の友達がほしいです。 After you made friends, for example: We are friends. = 私たちは友だちです。 I made / became friends with (someone). = 私は(someone) と 友達になりました。 I have American friends. = 私にはアメリカ人の友達がいます。 You can also say: 友達ができました for "I have friends / I made friends" in the place / country / school, like アメリカ人の友達ができました / 学校で友達ができました but with the specific person, we say (someone)と友達になりました. You can use 友達を作る almost as same as 友達ができる, however, I would use 友達ができる, and 友達します doesn't exist. One more thing, the particle after 私 is は and it's pronounced わ. I hope this was helpful.

作る is 'to make', する is 'to do'. also is used to turn nouns into verbs, like 仕事 -- 仕事する 'work' - 'to work'. About friends: you can 友達(を)できる as well as 友達(を)作る. They both mean to make friends.　But not 友達する.