What are you interested in? Working on e.g. the Linux kernel if your interest lies in user interfaces won't cut it. Preferably something you use day to day, so you have a feel of the problems, and are in some way connected to the user community.
Check the webpages for the packages of interest, take a peek at their developer lists and bugtracking systems. See if they advertise "tasks for newbies" or similar. Pick some simple tasks and work on them. Be careful to use the programming style used in the project, be it by looking at the code or check for official standards. Follow whatever style is in use for commit comments and other documentation.
You might get lucky and find a mentor, but don't count on it. Mentoring is a lot of work, which might not pay off. Besides, computer geeks are a reclusive breed. You'll have to make yourself known by judicious participation in the mailing lists or wiki.
Most of your proposed patches will just be silently ignored, you might get yelled at for others. A thick skin, and keeping cool when the flamewars start, is a must.
Perhaps you could check the "participate" pages for your preferred Linux distribution (or BSD. or whatever system you like), like Fedora's.