Open the app, and navigate to the profile tab (it's the one on the far right). Once there, click on the cog in the top right. From there, you just need to locate the 'Private Profile' section. From there you can adjust the slider to make your profile public or private.
Making your profile private won't affect your existing followers, but will require you approve new followers.
A word of warning though: you won't appear in the search function or in the recommended users tab if you opt to make your profile private.