The best introductory reading materials are the Wikipedia pages for Open Science and Open Research. You may also want to watch Michael Neilson's TedX Talk from 2011.
There is also a summary of Open Training for Open Science from late 2014.
Data Carpentry provides materials and lessons for domain specific areas including ecology, genomics, geospatial, sociology, and biology.
Open Science Training Initiative. This lecture slides and notes are available from thier GitHub repository. There are also videos of their 2013 lectures.
Software Carpentry provides videos and materials with an emphasis on version control, MatLab, R, and Python.
Software Carpentry offers workshops.
CREP - Collaborative Replications and Education Project crowdsources replication for undergraduate researchers. Small research awards (under 500 USD) are available.
The twitter feed @openscience for those developing short attention spans.
A continuing discussion of available resources on Quora.
Again, read the Wikipedia pages for Open Science and Open Research. These articles inclue a number of references to projects, initiatives, and organizations.