New to Obedience/ Agility showing

i dont know much about it so i cant help much.. but here is the AKC's sites on competive obedience and agility maybe they can help a bit []  [linkhttp://www.akc.org/events/obedience/index.cfm]http://www.akc.org/events/obedience/index.cfm[/link]
[linkhttp://www.akc.org/events/agility/index.cfm]http://www.akc.org/events/agility/index.cfm[/link]

I don't compete in obedience, but I can tell you the agility titles:

Novice
Open
Excellent

There are 2 types of classes offered in agility, either standard or jumpers. The standard classes offer all the obstacles, such as A-frame, teeter, dog walk, jumps, tunnels, table, weaves, etc.  The jumpers classes do not have any contact obstacles, only jumps, weaves and sometimes tunnels.  In order to get a title, you need 3 qualifing scores.  A qualifing score varies according to what level you are competing in.  So esenetially you can get a novice standard title, novice jumpers title, etc, etc.  After you reach the excellent level you can begin earning points toward a MACH title, which stands for Master Agility Champion (or something like that, can't remember).  The MACH takes years to earn, you have to earn an un-godly amount of double Q's and points.  I have a few friends who have earned it. 

I am sure the AKC site has more info, but that is a quick overview....

Champion (or something like that, can't remember). The MACH takes years to earn, you have to earn an un-godly amount of double Q's and points. I have a few friends who have earned it.

 
There's also a Masters title in agility that requires 10 legs (Q's) after you get your Excellent title.  While you're getting your Masters titles (MX, MXJ) you can work on your MACH.  A MACH is earned by getting 20 double Q's (the dog must Q in Std and JWW on the same day) plus 750 points.  Points are based on full seconds under standard course time.  First place gets his points doubled; second place gets 1.5x points. 
 
The OP may also want to look into Rally. 

I just started competing in regular obedience.  In the novice obedience ring here are the following exercises you are judged on:
 
Heeling pattern on lead: the judge will command you to heel fast, heel slow, heel normal, halt(your dog has to sit), right turn, about turn and left turn. Not necessarily in that order though.
 
Heeling in a figure 8:  The judge will ask you to heel in a figure 8 around two people that are standing 6 feet apart. The judge will ask you to halt twice(dog needs to sit at the halt)
 
Stand for exam: You take the lead off your dog at this point. The judge will ask you to stand your dog and leave when you're ready.  You can touch them and adjust thier legs.  They need to stay while you walk 6 feet in front of them. The  judge will approach your dog and touch thier head, back and rump.  Then you can return to your dog in heel position.  Your dog cannot move thier feet at all during the exercise.
 
Heel off lead: You perform the same heeling pattern off lead as you did on lead.
 
Recall exercise:  You put you dog in a sit stay and leave them for the other side of the ring.  You call your dog to you.  The dog needs to come and sit in front of you.  Then you tell the dog to return to heel position. 
 
Long sit/Long down:  The dog needs to stay perform a 1 minute sit stay. And then a 3 minute down stay.  This is done in a group of dogs.
 
You should look into joining an obedience club in your area.  They're a wealth of information and thier classes are generally tailored towards preparing you for competition. 
 
Its fun!
 

there are other agility venues available than AKC that offer many different types of classes. USDAA focuses on fast, athletic dogs and is probably the most competitive venue; many serious USDAA competitors think the AKC agility is kind of silly and second class. NADAC focuses more on course flow and dogs and handlers having fun than on athleticism of dogs; and there are other venues such as CPE and UKC.

There are multiple venues for competition. There are what are called Companion dog events on the AKC, which sort of act as a descriptor for events that involve dog and handler partnerships to complete a task.  These events are found in multiple venues.  All start with easiest and move to harder.  Many dogs/handers are successful at the easiest levels, as difficulty increases the number of successful teams usually decreases.
 
Obedience events are typically precision based events.  There is a specific pattern each dog and handler complete.  The pattern is judged against a "perfect" performance in the eye of the judge.  Obedience titles typically start with Novice, Open and Utility.  Heeling, staying in position, coming when called, retrieving, jumping and finding objects all figure into the events. 
 
Agility is the obstacle course and speed as well as accuracy is required.  The same idea of precision comes into play but in a different manner.  This sport is less familar and multiple commands and verbal interaction with the dog are allowed.
 
Rally is a combination (sort of) of obedience and rally.
 
Tracking is available as well.
 
The next type of events are those based on the original purpose of the dog.   There are herding events, retrieving events, earth dog events, coondog events, gun dog and or field trial events, weight pulling events and coursing events.  Not all events are offered in all venues.  Some venues offer only one type of event  (AHBA American Herding Breeds Association only offers herding tests and trials).  There are the protection sport/work:  Schutzhund, French Ring, Mondoring, IPO etc.

How exciting! You've been training and forming a partnership with your dog! When you are confident that your dog can heel on and off leash, come when called, return to heel, and stay sitting, laying down, or standing still while a stranger approaches and touches him lightly on the back, then you are ready to try for a novice title in AKC with your registered dog!
 
You may have been in obedience classes and encouraged by your instructor to enter an obedience trial! They should help you find matches and informal 'show and go's to test your readiness. These informal 'practice shows' will allow you to see how your dog will do in a busy and sometimes confusing environment.
 
You will find out about events at the local kennel or obedience clubs. Many have websites and post there information on them. At the least you can locate clubs near you at [linkhttp://www.akc.org]www.akc.org[/link] , club search. They will at least have an email or phone contact, you could ask to be placed on their mailing list for upcoming events.
 
Read all you can, and before you enter a trial read the AKC Obdedience Regulations.
 
Don't have a purebred? Then look at ASCA.org, and UKCdogs.com as they offer obedience titles to mixed bred, and un-registered purebreds too!
 
UKC titles are fixed before the dogs name: such as UCDX Sasha
AKC titles are fixed after the dogs name: such as Sasha CDX, RA
ASCA titles ... we haven't earned those.
 
You earn a title by qualifying three times under three, or two, different judges.
Be sure to read and understand (or ask questions!) to the rules that govern the events.
 
Good luck! I hope you will find it a very enjoyable hobby. I've made wonderful friends, learned more about my dog ~ an myself, than I dreamed possible.