The most basic exam can prove to be the most difficult of challenges in your day if you've ever had an uncooperative child. Depending on the age of your patient, different approaches can be made.
Before the patient and/or parent arrives in the room, you should have all equipment set up in advance. Make sure to have an extra lead apron for a parent if they wish to remain in the room with the child. I always like to encourage this except when the physical presence of the parent seems to make the child more combative.
You should always attempt the exam without immobilization first. This doesn't mean you need to make a bad exposure. Use your judgement about the quality of your radiograph before you commit to the attempt. Better to try unsuccessfully without a radiation dose than to settle on a sub-par quality film and end up repeating anyways. Be sure to communicate with the parent about immobilization techniques and requirements of the procedure. This may encourage better parent participation because they just want to get it over with to minimize any emotionally traumatic experience the child may have to endure (i.e. the pigg-o-stat). Don't forget to ask the mother if there's a possibility she could be pregnant before letting her assist.
The table-top attempt:
Place an 8x10 or 10x12 cassette in a grid holder at one end of the table. At the other end, align the x-ray tube horizontally to the cassette. Consider placing a sheet over the cassette so the patient will not be startled because of its ice-cold tempurature. Have mom or dad put the lead on and have a small lead apron for the patient (a thyriod shield will work on small patients). You should already have a preliminary technique set up for the AP chest. Place the patient's back against the cassette and the shield over their lap. Mom or dad can hold the arms to the side, grasping mid-humerus, and making sure to keep the child's back flat against the cassette.
For the lateral, simply rotate the patient's legs to their left 90 degrees. Have a parent stand in front of the patient and grasp the arms at the elbows bringing them together to touch in front of the face, also ensuring proper elevation above the thorax. I typically like to increase the kV by 10% and double my mAs from the AP to the lateral, but everyone has a different rule of thumb.
At three years old, the pediatric patient may be too large for the pig-o-stat. If they are somewhat cooperative, you may be able to provide a foot-stool and stand them at the upright bucky. Most will not be able to perform a PA projection because they are trying to see all of the equipment and may be a little frightened to turn their back. I worked at a facility where we put a rather large "Shrek" sticker on the bottom of the x-ray tube to give them something familiar to look at for the AP projection. Another sticker was placed on the wall directly in front of them when they were in the left lateral position. All we said was "look at Shrek" and they cooperated, but you better be on the rotor because it didn't last more than a few seconds.
If you have an absolutely uncooperative patient that requires immobilization, the pigg-o-stat is the method of choice for radiographers. Most come with different sized adjustable flanks and you may want to sneak a peak at your patient before bringing them into the room to estimate the appropriate size.
If you've never used one or seen one, they look like some sort of dark-age torture device, which they could easily turn into if you let the patient sit in them too long. You simply place them into the seat with arms above their head and close the flanks. Make sure to lock them in place. If you have all of this set up in advance, the patient should be in and out in just a few seconds.