Race event points are scored in Official Series Races; the best 25% of a driver's race performance (based on points scored) in a given Race Week will be averaged to determine the points scored that week for each Official Series Race.
See the FAQ entry on Series Points for full details on how points are calculated.
You can view your race results at any time to see which races for a given series are counting toward your weekly and overall championship points totals and which races have been "dropped" by looking at your individual stats as follows:
From the main iRacing members page, select "Individual" from the STATS pull-down to view your career stats:
On the CAREER STATS page select "Event Results":
This will take you to the RESULTS ARCHIVE page, and from there you can view all of your race results for all series that you have participated in.
Your points earned will be shown under the "Champ Pts" column; results shown in red are dropped results that do not count toward the best 50% of your points for the week.
If you want to view only the results for a specific series, simply select the series that you want to view from the Series pull-down and press "Go." Note that you can filter the results further using the SESSIONS check boxes to filter out unofficial sessions, qualifying sessions, etc.