How does the poem "Song of Myself" combine the personal and the universal?
In general, the poem has two main themes: one is himself and how wonderful it is to be him-so that is a very personal theme. The other is nature and other people around him, and how wonderful they are, and how he feels a connection to them; how they are all part of the greater whole in the universe. That theme is universal.
There are many examples of both personal and universal themes throughout. For personal themes, consider section 1 with "I celebrate myself, and sing myself", section 5, "I believe in you my soul," section 20, "I know I am august (strong), I do not trouble my spirit to vindicate itself or be understood...I exist as I am, that is enough," and section 24, in which, in detail, he praises everything about himself and ties those things to everyone else too.
For universal themes look at section 17, "These are really the thoughts of all men in all ages and land, they are not original with me," and section 1, "for every atom belonging to me as good belongs to you," section 16, "I am of old and young, of the foolish as much as the wise...marternal as well as paternal, a child as well as a man."
Those are just a few examples of the personal and universal in "Song of Myself"; there are many, many more, but I hope that gets you started. In all of the poem, Whitman does celebrate himself, but always with the connectio to the universal; he is glorious, but only because he is part of you and me, nature and the universe. He is who he is because of everything else; so that is the connection between the two. Rarely does his singularly praise himself without tying it to others, nature, life and the universe.