If the club is using TOD, you do need to know the distance of the race to determine the correction amount, and then subtract it to get the corrected time. If TOT is used, the formula (see Marty's post above, if it is correct- I haven't checked) the distance doesn't matter. The handicap is based on how much time each boat took. Adjusting for the standard windspeed generally helps the slower boats to be more competitive.
Since you don't seem to be able to get anyone to give you answers on how the results are tabulated, it sounds like the club is using TOT, and probably a program like Sailwave (it's free, and really good) to calculate them. The RC plugs in each boat's name and rating at the beginning of the season, and then adds the start and finish times for the boats in each race. The program spits out the result, including series scores. Our racers are pleased that it also uploads to the club webpage, so they can get the results form their cellphones before they've even finished folding their sails.