The UK Information Commissioner's Office has produced an excellent explanation and chronological table of the procedure in the European Union for passing (or not) the proposed data protection law reforms. (The same procedure is used for most other proposed EU laws too.)
The detail-inclined can read more about the so-called ordinary legislative procedure (used to be called "codecision procedure"):
- EU page on the ordinary legislative procedure (and EU decision-making more generally)
- The Danish EU Information Centre's explanation
For the visually-inclined, here are some flowchart graphics (or infographics, to be trendier!):
Diagram above (from the above codecision report) contains Parliamentary information licensed under the Open Parliament Licence v1.0
Diagram above (from the Word version of "How the European Union Works") as per the Europa site's copyright notice
And flow chart from another Europa webpage, as per the Europa site's copyright notice
Bottom line - judging by the volume of European Parliament amendments proposed so far, there's a long way to go yet…