Here are some slides on how to get start with contributing to Sage; and here is a version of the slides hosted on github: Getting Started With SageMath Development.
We prepared some worksheets for the tutorial sessions at various Sage Days events. I converted these worksheets so that they can be used on SageMathCloud. Download them from this SageMathCloud project.
At Sage Days 45 at ICERM, Anne Schilling, Avinash Dalal, Allen Knutson and I implemented a solver for various types of Knutson-Tao puzzles. The code was merged in Sage version 5.10 (2013). See ticket #14141 for more detailed information.
Building on work of Nicholas M. Thiery and Jason Bandlow, Chris Berg and I implemented the Hopf algebras of non-commutative symmetric functions and quasisymmetric functions in Sage. The code was merged into Sage version 5.4 (2012). See ticket #8899 for more detailed information.
I wrote some code to work with the Hopf algebra of supercharacters of the groups of upper-triangular unimodular matrices over a finite field of size q. More information and instructions on how to use and obtain the software can be found here.
Sage Days 20.5 will be a 5-day intensive workshop to develop and implement algorithms for research in algebraic combinatorics and the representation theory of finite dimensional algebras.
I wrote Sage code for creating irreducible matrix representations of the symmetric groups. The code is based on the method described in the article Young representations of the symmetric group by Alain Lascoux and was been merged into sage-4.1. (This last link includes information about this new functionality.)
I gave an 18-hour short-course on Sage at the Universita di Siena in May 2009. The lectures were delivered in Italian, but all the worksheets are in English.
I have given a few talks on Sage, you can find information, together with slides and Sage worksheets, under presentations.
Update 2 (18 July 2009): A major refactoring/reworking of the above code will be merged into sage-4.1.1. (Note: the above link points to the release tour page that summarizes the changes in the sage-4.1.1 release; the release is scheduled for early August, so the link probably won't work before then.)
I taught a short, intensive (5 days, 3 hours/day) mini-course on Sage in May 2008.
Peter Jipsen and I have started to work on adding support for posets to Sage. Keep track of our progress on the ticket on the Sage trac server. (Update: this patch has been merged into sage-3.0.2. More features to be added.)