Decide on scoring before you start. Yes, disc golf generally scores the same as "club" golf, one point per stroke, lowest wins, but some players may also have their own "house rules" about scoring, since disc golf is a little more informal and quirky than the original.
Use the basic "stroke-play" scoring of one point per throw, and tally up the scores for each "hole" or in this case basket, separately. Disc golf also includes "par" for each hole, which is an interesting addition if the pars are available on the course.
Allow funny "special scoring." Special scores can be a fun part of a disc golf game as long as they're agreed upon before hand. Examples include, 5 points for retrieving a tree shot, or half points for throwing from a sitting position. You can also use handicaps, as in regular golf, to keep different player strengths competitive.
Use other scoring methods like match play and speed golf. In match play, the only score kept is one point per hole for the player who finished that hole in the lowest number of throws. Match play can be a more direct way of scoring the game, and more challenging.
Use the Disc Golf Score Recorder. This software for Microsoft Windows offers game tracking and game analysis for disc golf. It's available online at a "quick buy" price of $34.95; screen shots and descriptions are available on the website.