As with most things pediatrics, techniques vary widely by age and there's a good chance you won't feel like a nice person afterwards.
TM: I feel your pain. Infants and toddlers (3-24 months) are easier to lay down on the exam table by having Parent help by placing hands on shoulder joints and forearm over elbow joint immobilizing arms, and either let 'em kick or have Parent lean her belly or elbow over the thigh. This gives you whole hand against the kid's temporal area to immobilize the head. This is harder to do with young kids, but still possible (and necessary) with most 2 year olds and many 3-4 year olds. I usually give Parent some task like sing the kid's favorite song to take their mind off things and convince them they aren't torturing their kids.
When doing the otoscopic exam on the parent's lap, I am very particular about my Parent holders. If I want to look at the left ear, the kid is sitting on Parent's left thing with lower legs dangling between the parent's thighs and immobilized by Parent's leg adduction. Parent's right arm is wrapped around the kids torso and arms, and the left arm around the head and forehead to try and prevent the kid's head from burrowing into the chest. Again, the parent is talking to the kid the entire time, and I usually give Parent a specific task to calm them down, which hopefully sends calming vibes to the kid. Developmentally, kids become more social and rely on parental cues more in early childhood as they leave the stranger anxiety phase, so making Parent laugh never hurts.
I've heard different things about oto-tip placement, but I like starting out having mine right at the opening of the auditory canal. It gives you as little more freedom to angle the otoscope posteriorly and superiorly to see all four quadrants of the TM. Also, if there's wax, you see it while it's still superficial and before you jam it close to the TM. Additionally, if the kids ears are clean and if it's an easy shot, it may be less painful.
Sometimes, however, you have to advance it all the way end, especially if there's an especially prominent posterior bend in the canal. If you feel like you can see the posterior TM but not the bottom or anterior, I've found it's usually fixed by advancing the otoscope to get better angle around the bend in the canal. If you can't see ANY land marks, you may actually looking at the interior portion of the canal. With the reflection of the light it sometimes looks like otosclerosis or a dull TM, but really its just skin, angle the oto tip anteriorly or posteriorly to explore further.
Lastly, with 2-4 year olds (especially the older end of the range) kids can be surprisingly cooperative if you butter them up. They may not even need any holding/positioning. I usually ply them with bubbles. Young children are suckers for bubbles.
The G**D***ed Oropharynx: This is always the last item on my exam. Why? Because if they're crying after the TM exam then you have an amazing view of the tonsils. Other little tips:
1) You open your mouth wider if you look up. Do something to make the kid look up while his mouth is open.
2) Press on the checks with you thumb and fore finger. Having your oral-mucosa pressed against teeth is unpleasant and kids reflexively open their mouths.
3) If you use a tongue depressor, be decisively fast. Take a mental picture of the tonsils and think about what you saw later. Most kids reflexively bite down as soon as the depressor is on the tongue.
4) Make the kid cry. Usually accidentally gagging them from the tongue depressor does the trick. As DeadCactus said, they are non the worse for the wear afterwards. Also take advantage of the kid crying for any other reason (e.g. seeing a vaccine needle, mom leaving the room etc).
Oh ALSO! Given that it's now summer; when looking at throats, and you can't see the tonsils yet, take advantage and make sure you look at palate. I've already seen two cases of herpangina / coxsackie virus this year.