Here is my data from that night. This is what a night's observations becomes after a few hours of hard work processing it:

COD 735
CON William G. Dillon, 4703 Birkenhead Circle, Missouri City, TX 77459, USA
CON [Asteroid-Team@yahoogroups.com]
OBS J. Dellinger
MEA J. Dellinger
NET USNO-A2.0
TEL 0.46m f/4.5 Newtonian + CCD
BND R
ACK 2003 HN15 and -31 Dec search fields. OBS disc if unknown.

     F35281 * C2003 05 28.17977 16 38 39.59 -06 56 00.0          17.5 R      735
     F35281   C2003 05 28.19801 16 38 37.85 -06 56 18.1          17.6 R      735
     F35281   C2003 05 28.27449 16 38 30.57 -06 57 33.1          16.7 R      735
     F35282 * C2003 05 28.18284 16 39 36.06 -07 07 08.4          18.5 R      735
     F35282   C2003 05 28.19161 16 39 35.54 -07 07 10.7          19.3 R      735
     F35282   C2003 05 28.27449 16 39 30.29 -07 07 33.2          18.4 R      735
     F35283 * C2003 05 28.19161 16 39 47.23 -07 14 13.9          17.2 R      735
     F35283   C2003 05 28.20197 16 39 46.58 -07 14 12.3          17.4 R      735
     F35283   C2003 05 28.21321 16 39 45.92 -07 14 10.1          17.4 R      735
     F35284 * C2003 05 28.18284 16 40 03.76 -07 10 29.1          18.5 R      735
     F35284   C2003 05 28.20197 16 40 02.84 -07 10 24.3          18.1 R      735
     F35284   C2003 05 28.27449 16 39 59.33 -07 10 07.8          18.3 R      735
     F35285 * C2003 05 28.23331 14 49 04.62 -31 04 20.8          18.1 R      735
     F35285   C2003 05 28.25013 14 49 03.74 -31 04 20.5          17.9 R      735
     F35285   C2003 05 28.25948 14 49 03.16 -31 04 20.0          18.5 R      735
     F35286 * C2003 05 28.22618 14 48 11.74 -31 06 18.1          17.4 R      735
     F35286   C2003 05 28.23331 14 48 11.37 -31 06 14.1          17.3 R      735
     F35286   C2003 05 28.24080 14 48 10.95 -31 06 10.0          17.2 R      735
     F35287 * C2003 05 28.22618 14 49 35.91 -31 16 38.4          17.0 R      735
     F35287   C2003 05 28.23331 14 49 35.57 -31 16 35.1          16.9 R      735
     F35287   C2003 05 28.24080 14 49 35.19 -31 16 31.7          16.8 R      735
     F35288 * C2003 05 28.25013 14 48 42.90 -31 16 49.6          17.1 R      735
     F35288   C2003 05 28.25948 14 48 42.47 -31 16 46.1          17.0 R      735

The first column is a unique identifier that each observatory gets to make up for itself. We used "F" for "Fort Bend Astronomy Club", then a single digit for the year (3 = 2003), then the month (5 = May), then the day of the month (28), then a character for each object observed. "Claerbout" was object 2 that night, hence "F35282". The "C" just means "CCD camera", then the year, month, and day (to the nearest second). Then the Right Ascencion (RA) in hours, minutes, seconds, then the Declination (Dec) in degrees, minutes, and seconds. Then the brightness, a letter indicating what color the observation is sensitive to (for our CCD camera R for "Red"), then the observatory's code (we are "735").

If you bring up http://www.minorplanetcenter.org/iau/MPEph/MPEph.html and type in Claerbout and check "MPC 8 line" and "show residuals" you can see a list of the observations used to determine the official orbit. You can see these observations from 28 May 2003 were pretty good. The "residuals" columns are date, observatory (again, "735" is us), error in RA, and error in Dec (both in arc seconds). You can think of RA as "longitude in the sky" and Dec as "latitude in the sky". Generally they want your observations to be good to within 2 arc seconds, 1 if possible.

Observations in parenthesis are outliers dropped from the orbital fit. Other team members shot the object June 1... they clearly had a problem with their clock that they didn't catch!

As you can see others had imaged this object in 1997, 2000, and 2002, and even earlier in May 2003, but their nights were never closely spaced and the minor planet center didn't figure out to put the points together. We got a closely spaced set of nights from 28 May, 29 May, and 31 May, which clinched it.

Here is what we got back from the MPC after turning in that night's data:

F35281  (K00A93C    F35283  (10962      F35286  (K00X07A    F35287  (15925
F35288  (24030

This is basically a list of which objects they recognized. From the eight we turned in, they didn't recognize 2, 4, or 5. We attempted to get followup nights on all three, and were successful on 2 and 4. Here's how the MPC lets you know you have a discovery credit:

F35282   K03K18X    F35284   K03K18Y    F35291  (K03K18Y    F35293  (K03K18X

This means "we recognize that F35293 is the same object as F35282 and we still don't recognize it so we are assigning the new provisional designation 2003 KX18". The lack of a left parenthesis means it's a new designation. (Hence "the dreaded left paren" meaning "not a discovery after all".) (And similarly we got a pair of nights on 2003 KY18.)