Hello!  This is a great question and on a topic not often touched on at Education.com  As a parent of a now young adult actor, I can tell you that there is much to learn when you and your children venture down the road of the entertainment industry.
 
First and foremost-  NEVER, NEVER, EVER pay for an audition.  There are people/businesses out in many communities that promise to get your child in front of top casting directors if....1) you pay for an audition or 2) pay for headshots/professional photography or 3) pay for expensive acting classes that often put parents in debt.
 
Reputable agents, managers and casting directors do not ask for fees for auditions or "go sees".  Agents and managers make their money from payment from companies that cast an actor for on camera or print work.
 
Now let us look at your children and their ages.  Four year olds do not need formal acting classes.  I have helped agents when they are seeking new talent and they often want to see children who are natural, able to take direction and can be patient when there is a long wait.  (The entertainment industry is full of hurry up and wait situations!)  Many times casting agents are looking for children who are comfortable and at ease when there are many people in a room.  They also like to see children who are quick witted and think fast on their feet.  Early readers are a plus.  Having skills such as bike riding, being at ease with animals and good speech skills is a plus.  Missing teeth and glasses are sometimes an asset vs. a problem.
 
  My understanding is that older children who look younger have a better chance at longevity in this business.  Thus, if your 12 year old can play the role of a ten year old that might be good.  Twelve is a tricky age in the entertainment business.  It was the age my daughter started and she was often dissuaded by people as the field is flooded with pre-teens and young teens who want to be "discovered".  However, a young teen that has a confidence, has had experiences that will help him/her to stand out, such as athleticism, musical ability, multilingual or an unusual look, may excel over others.  One must for all student aged actors is that they need to be good students.  My daughter was often asked if she was a B average student or better.  You may wonder why?  The answer is that there are laws that ensure that child actors (up to high school graduation) receive education while being involved in filming/print work during school hours.  Sometimes, a tutor will be ordered to work with the child during the day.  These laws are especially enforced if the child has been employed on union sets and needs to join the Screen Actors Guild (SAG), the American Federation of Television and Radio Artists (AFTRA), Actors Equity (AEC).
 
Here is what a family starting out should know...
 
1- Make sure that your child or children want to go down this road.  It is paved with hard work, rejection and very little financial benefit for most.  Often the hours are long and families need to be committed.  I recall needing to cease full-time employment so I was able to drop everything at a moment's notice and rush with my daughter to an audition 100 miles away from home.
 
2- Make sure to check for casting calls that are legitimate. Always accompany your children. (Same for when they get work and are on sets as this is the law).  I have supplied you with websites below that should have important legal and casting information.  Please read them.  
 
3-  Again.... never pay for an audition.  This should be a mantra for all parents of actors.  Temptation is great as people will promise you the sky if you pay, however, don't.  Disney has a specific casting process and expensive acting classes that parents often can't afford is usually not the guarantee to being the next Hannah Montana.
 
4- Have your child read a lot.. aloud.  Let them be comfortable with simple one minute monologues (Available at bookstores or libraries).  Good reading and memorization skills are key.
 
5- When you get a call to audition remember that it is a competition.  Usually only a few people (or maybe one) "wins".  The others go home and get to practice and start again.  Sometimes you will audition and not hear anything for weeks then "the" call comes in that your child got the role. Be prepared. Truly anything can happen.  Also, an agent once told me something very smart.  When you go to an audition pack a bag and be prepared to stay.  Have extra headshots and resumes, a change of clothing and anything important, especially if you are traveling a distance for this audition.  A few times I would drive with my daughter to a city 150 miles away and then leave only to get a call from her agent that they wanted to see her again later the same day for a "call back".  This is in essence the second part of an audition process where they have dwindled down their selections to just a few candidates.  
 
6- Your family needs to be all in agreement about pursuing this industry.  There will be times when one child (and it could be only one of the twins) will get several auditions while the others do not.  Boys are more in demand than girls as the competition is less. At an open call recently the girls outnumbered the boys 3 to 1.
 
7- When you get a job be a good parent on the set and have your child demonstrate excellent patience and congeniality.  Complainers, people who do not follow directions and those who are only trying to get work for their children to meet celebrities are often not asked back. Chances are first roles will be those of an "extra" and you will find that exemplary behavior can be of benefit.  (This includes parents too).  One time, my daughter was on the set for a major television show.  We were told not to bring any cameras.  One father did and then hounded some of the "stars" for photos with his son. They were sent off the set.  Later that same day, the director noted that my daughter was very friendly and had a real interest in filmmaking.  He invited her to watch the acting from behind the cameras when she was done with her scene.  To this day I believe that helped her decide that behind the camera was as exciting to her as in front of the camera.
 
8-  Make a support system with parents you meet.  About five years ago I was lucky to accompany my daughter on to a set of a small independent movie that she had been given a small role.  The hours were long.  The cast was usually just a dozen or so at any time.  I met wonderful parents and many of us remained friends to this day.  We know that often our "kids" are up for the same roles, but all agree that we wish each other the best of luck and champion everyone's success.  If you go in to the business with this attitude and your child actor has the same then the experience is far more pleasurable.
 
Enjoy the websites below. the listing for Brian Dragonuk is for the east coast.  He has a wonderful listserv that is top notch.  Each of the websites below has different information.  Also, you may wish to peruse http://www.IMDB.com for fun.
 
Good luck and break a leg!
 
Louise Masin Sattler, NCSP
Nationally Certified School Psychologist
Owner of Signing Families
http://www.SigningFamilies.com