Android Studio 3
The answers that talk about Maven Central are dated since Android Studio uses JCenter as the default repository center now. Your project's build.gradle file should have something like this:
repositories {
google()
jcenter()
}
So as long as the developer has their Maven repository there (which Picasso does), then all you would have to do is add a single line to the dependencies section of your app's build.gradle file.
dependencies {
// ...
implementation 'com.squareup.picasso:picasso:2.5.2'
}