1) When you actually fly on an airline on a paid ticket (which would include one booked with UR points, but not the airline's own frequent flier points) you can earn miles on that airline or its partners. So if you take a 2000 mile trip on American, you can earn 2000 miles on American, British Airways, or other OneWorld airlines.
2) When you buy any ticket with your CSP card, you will get 2 UR points per dollar spent.
3) If you book travel on the UR site, using the UR interface, you will get 3 UR points per dollar spent. I strongly discourage this, as the UR interface often does not have the best schedules and fares.
4) If you go to the UR site and then to the UR mall, you can click through to sites like Orbitz, Expedia, and Travelocity, and get bonus points. Travelocity gives 2x points so you would get a total of 4 points per dollar spent. Cross-check the fares though, particularly for international trips, as some of these sites have fees. Mostly the fees are for trips on multiple airlines or for trips originating outside the USA.
5) If you choose to, you can redeem UR points for travel on the UR site at a ratio of $0.01333 per point. So if you have 30,000 points you can get a $400 ticket. Many people can get better value for their points by transferring to an airline or hotel partner, but for other people it's easier to just take the quasi-cash and be done with it.
So anytime you fly, you should have a FF number in your reservation, and most likely the main USA airline available (i.e. use American if flying American, BA, Quantas, etc.) except that if you are going for elite status on a partner, you might use the partner (i.e. if you want elite on United and are flying USAir, credit it to United).