This is going to depend a lot on the sport. In general, a reporter does have access to several resources, many of which are accessible to a dedicated fan, but when putting together commentary on the spot it helps a lot to have deep personal knowledge of the sport to consider what facts to research. (This kind of knowledge can be developed by a fan regularly reading publications like Track and Field News, Athletics Weekly, and/or the IAAF website.)
I've covered athletics (track and field) at the 2008 Olympics in Beijing and six IAAF World Championships starting in 1999, as well as many lesser meets. This is a rough overview of the compiled resources available to an athletics writer:
All of these resources are available to a dedicated fan, many for free and the rest for a relatively low price. The bound annuals are probably the most expensive due to printing costs, and as more and more publication moves to the web the books are increasingly available as PDFs. Membership in professional organizations like the ATFS (Association of Track and Field Statisticians) or TAFWA/FAST (Track And Field Writers of America/Federation of American Statisticians of Track) in the USA often provides access to additional resources; I get PDF or bound copies of the world and USA annuals either through TAFWA or through the national and international federations.
At the bigger meets, an additional resource which isn't available to the fans is what's known as a CIS or Commentator Information Service. This is a terminal in the press section which gives access to live results, entry lists, splits, and some historical data. Increasingly the same information is appearing on event websites - the IAAF website has almost the same data online as in the CIS - but as a dedicated on-site system the CIS isn't subject to the same kind of network latency a website usually shows.
Being on-site also allows the press access to information which programmers would call "asynchronous," that is, not happening within view of the camera. This includes things like post-event disqualifications and protests.
I assume similar resources are available to stadium sports like swimming and tennis. Outside-stadium events like marathons, race walks, and (I assume) road cycling or skiing have additional challenges in that spectators and reporters alike have severely limited information about the progress of an ongoing event. As an example, both the Boston and New York City marathons have elaborate systems of spotters on bicycles reporting information back to the press room to help television commentators understand how fast the leaders are going, and even who's in the pack. Every event faces different challenges in collecting this kind of detailed information and communicating it in a useful way; journalists are usually the first to get access to the data.
ETA summer 2016: With the US Olympic Trials for athletics approaching, I was reminded of another source of information: dedicated insiders who are self-publishing. The specific example I had in mind is the decathlon association which has published a "media guide" for the decathlon and heptathlon at the Trials; this is packed with lists of previous winners, all-time best performances in each event, at an Olympic Trials, at a national championships (the Trials doubles as the USA national championships), or at Hayward Field where the Trials are being held. The majority of this is the work of Dr. Frank Zarnowski. The multi-events even have "prediction sites" where curious fans can plug in various scenarios of athletes' performances in each event and see how the overall event would play out; an example (which used to live at the ergorej.net domain) is the Beijing World Championship decathlon in 2015 where Ashton Eaton set the world record.
ETA 2: The IAAF statistical handbook for the 2016 Rio Olympic Games has been published now (that link is to a PDF download).