Are you using a game engine? If yes, your game engine likely comes in with a built in post-processing system/pipeline, in which case you shouldn’t have to worry about frame buffers for simple post-processing.
If your engine doesn’t have a post-fx system, or you’re making an engine from scratch: yes you would use a quad. The key, is that instead of rendering/transforming the quad in world-space you would render and position it in view-space so it will be fixed in the screen instead of in the world. You’ll do this changing whatever transformation matrix is being used to displace the quads vertices to a view-space-matrix.
You might want to familiarize yourself with the purpose of matrices (which effectively act as stores for transformations in 3D games) and the basic graphics / shader pipeline.
Here’s a link which offers an overview of the role of matrices and spaces in realtime 3D rendering.