WordPress uses Subversion for source control. You will want to check out a working copy of WordPress using a Subversion client (such as Tortoise SVN on Windows, using the command line on Mac and Linux). For more, read the Subversion article.
One of the many benefits to using a version control system is that you can create a simple text file, called a patch, that shows exactly what you’ve changed – the lines of code you added, modified, and removed. A patch is also called a diff, for differences.
If you are not familiar with how WordPress is written and organized, read the article on the WordPress Codebase.
Once you’ve figured out how to fix the bug by modifying WordPress core files, you should create a patch. Review the Creating a Patch documentation.
Once you’ve created a patch, upload it to the Trac ticket using the Attach file button, and add has-patch to the workflow keywords. Please don’t overwrite any existing, previous patches.
Look through the ticket report for “early” tickets. These tickets have been marked by contributing developers as needing attention early in the WordPress release cycle. Generally, this means a trusted core contributor has shown interest in it, “blessing” the ticket to a certain extent.
Look through the Awaiting Review report. These tickets have not yet been slated for the next release of WordPress, but if a developer takes an interest in it, that can change.