I am familiar with the notion of Lie groupoids. 

But, only easy examples of Lie groupoids I am familiar with are the following:

 1. Lie groupoids coming from manifolds; that are of the form $(M\rightrightarrows M)$.
 2. Lie groupoids coming from groups; that are of the form $(G\rightrightarrows *)$.
 3. Lie groupoids coming from an action of Lie group on a manifold, say $M\times G\rightarrow M$; that are of the form $(M\times G\rightrightarrows M)$, also called as translation Lie groupoid.

To understand some structure over a Lie groupoid, I would first see their special cases in above examples. This gives some understanding of what the structure is in some special cases. There is a theorem by Ieke Moerdijk and D. A. Pronk that says [that][1] any proper étale Lie groupoid is locally a translation groupoid. 

Are there other simpler Lie groupoids that you use in the same line of above mentioned Lie groupoids that gives a better understanding of a setup on an arbitrary Lie groupoid?  


  [1]: https://mathoverflow.net/questions/303183/proper-and-etale-groupoid-is-locally-a-translation-groupoid