You can finish most decent dogs in a weekend of UKC shows. You have to have 100 points. Each time in the ring gets you 25 points, win lose or draw, competition or no.
You also have to have at least 2 wins WITH competition, meaning you must defeat at least ONE other dog. I think its 2, might be 3, I would have to go look.
AKC is much harder. The most points you can win at a time in an AKC show is 5, and it takes 15 to make up a CH, and yes, you must have the 2 major wins in AKC. Points are calculated according to the number of each sex in competition for the points. Majors are 3 points or more.
Congrats again on your new U-CH!