Hmmm, well showing in conformation is something that takes a lot of planning from before you get your first Chi that you want to show. The breed standard is very specific (I like looking at this extended version of the standard as it's much more specific than what is on the AKC website: Chihuahua Extended Breed Standard
This is if you're wanting to show in AKC conformation shows. First you have to find a dog that is a fine example of the standard. We've just started showing Lulu...took a good year to find a pup suitable...and even then I continued to learn about standard...still am! It's always a gamble when buying a puppy to show because they change so much & could turn out not quite what you thought or not quite what they should be.
Anyway, after you study the standard & then find a suitable pup than I'd suggest contacting your local kennel club. I think CO is like us in ME...they pretty much only offer handling classes in the warmer months. To find shows I use infodog.com though you can also do a seach on the AKC website for events. You could also look there & see where/when there are shows near by you could go watch. Doing that before actually showing (or even before buying your dog to show) will give you an idea of what type of dog/bitch is winning in your area. Unfortunately there is more to it than getting an AKC registered dog & just wanting to show it. MANY (most actually) AKC dogs are not suitable for the show ring to be honest.
I'm not sure where your new pup comes from but to get a pup you'd like to show, unless you already have an eye for the breed standard & know exactly what you're looking for, I'd recommend finding a breeder who shows their breeding stock & knows what you are looking for. They could better assist you & help you get what you want if you're serious about showing.
There is also AKC obedience or agility trials rather than conformation shows which may be more of an interest to you? It's not so much focused on looks so much as training & "fun". (don't get me wrong...I think showing in conformation is fun & rewarding...but a different kind of "fun" and a different kind of training/classes are required!
) Either way, if you contact/join your local all breed KC they should be able to point you in the right direction.