How to sponsor a new contributor
Sponsoring Someone for Fedora Package Collection
Sponsoring someone for access to Fedora Package Collection is relatively simple. If you are looking for someone to sponsor, take a look at the Fedora Account system for contributors who are currently searching for a sponsor. Note that they should also have submitted a package review request for a package which they are proposing to add to Fedora on  . In this request they should write, that they need a sponsor.
Bugzilla will send a notification mail for the new review request to the fedora-package-review mailing list. Take a look at their package and review it. If it looks reasonable and it seems that the comply with the Packaging Guidelines , then they are probably a good candidate to be sponsored.
Add any comment for changes to the review request on Bugzilla which look as though they'd be needed for compliance as well as the fact that you're volunteering to sponsor them. Once they've made those changes, you can approve the package and click the appropriate link to sponsor them for access.
A new packager cannot, at this time, make changes to packages he does not own or comaintain until he applies to become an Überpackager (see below) but you should still keep an eye on them. You should be sure to review their commits to the CVS repository for how they look, and consider watching their Bugzilla activity at least for a while (Account->Email->Users to watch). Respond with any comments that you might have and guide them, providing assistance as they need it for any tasks.
So what's the downside to sponsoring someone? Your sponsoree will likely have questions about processes; one of your responsibilities as a sponsor is to help them with the answers. A sponsor isn't expected to be omniscient, though, so you can feel free to ask for others' advice and opinions if you get a really hard question.
Sponsoring someone to become an Überpackager is a much simpler process. Generally people looking to become Überpackagers should have been around for awhile. If someone asks you to sponsor them as an Überpackager you should simply go with your feeling based on having interacted with them in the community in the past. If it is someone that you have not had much contact with, you might want to ask on IRC or look through bugzilla to see what kind of work the person has done. All you are checking for is sanity. As long as there are no "Support more internets on a single tube" RFEs in their history, you should probably go ahead and sponsor them. You should also be wary of sponsoring packagers who haven't been around long, and the packager should be able to tell you a specific reason as to why they want this access.
Unlike initial sponsorship, sponsoring someone to become an Überpackager does not confer as much responsibility on you. It is generally a one time ask-and-receive interaction.
Becoming a Fedora Package Collection Sponsor
Fedora Package Collection has been setup so to encourage "learning by doing" and the development of cooperative relationships between Fedora packagers. To date, advancement to a sponsorship position has been an undocumented yet somewhat formal process. Within the project, people have (and continue to!) develop reputations by creating packages, performing reviews, helping others with their questions, and generally doing what they can to advance/improve Fedora packaging.
When someone within the project has developed a "good reputation" (and this is admittedly a somewhat fuzzy definition!) then someone else will generally nominate them for sponsor status. You can also self-nominate if you feel you have the ability and want to take responsibility for helping train new packagers. Nominations can be sent to the fedora-devel-list , directly to the Fedora Engineering Steering Committee Chair, or in-person during the appropriate portion of a Steering Committee IRC meeting. A discussion and vote will then occur during the next Fedora Engineering Steering Committee meeting.
How To Get Sponsored
If you are looking for more information on getting sponsored yourself, take a look at http://fedoraproject.org/wiki/PackageMaintainers/HowToGetSponsored