I want to develop a library for Android. In what form can I ship it? jar, apk or something else? How should I do it so that other developers can use my library in their applica
If your library is pure Java code, a JAR is fine, perhaps ZIPped with documentation, etc.
If you need resources or other Android-specific non-Java stuff, you should look at using an Android library project. That is best shipped as source code, though there are tricks for packaging it up in (mostly) binary form. And the new Gradle-based build system under development should make it easier to create library projects that ship in binary (non-source) form.