Question: My toddler doesn't like to get his teeth brushed. How do I get him to be more cooperative?

He knows it's part of the bedtime routine and doesn't try to avoid it. He will happily grab and hold out his toothbrush for us to put toothpaste on it, and then he enjoys sucking and chewing it. 

When he's done that for a short while, we decide it's necessary to do it properly, and that often ends in me holding him while my wife brushing his teeth, while we explain what we're doing and why. It only takes 20 seconds, but it's always accompanied by screaming and squirming. I'd like to find a way to avoid this. As soon as we're done, everything is fine again.

**Clarification and update:**  

At this age, we don't expect him to be able to brush his teeth on his own. What I meant was that he didn't allow us to do it for him either. 

In the meantime, four months have passed since I asked this, and he's developed a lot. Now he gladly lets us brush his teeth carefully and cheerfully. 

**Update 2:**  

Another 6 months have passed, and he's still not enjoying the experience. He understands that it has to be done, and he sees us do it too. Sometimes he'll happily let us brush his teeth, other times it's a struggle. 

We are using several suggestions from the answers below -- we sing, we distract, we talk about "dirty teeth" and brushing the "dirty sugar" away, we let him brush on his own for a while and then take over, he can see himself in the mirror, etc.
All of this helps, but one factor certainly is that he's tired, and that's natural because brushing teeth is part of the bedtime routine.

Answer: 
When those first pearly whites emerge (or even before) begin using an Infadent brush. This soft sleeve with fine bristles fits over the tip of an adults finger. It is dense enough to protect from bites and feels good to gums. And, it comes with an "infant" toothpaste and is easily cleaned.

Then, graduate to a vibrating toothbrush. The vibration is of great benefit to ones with oral sensory sensitivities and makes toothbrushing fun. 

Toothbrushing requires refined motor movements. Toddlers are just learning to move one hand across the midline of their body (the preceding developmental level is moving hands together at midline). Making refined short movements in a tiny space (the distance of the horizontal surface of a tooth) are difficult. They have just learned to hold a spoon and hitting their mouths (maybe). And making squiggly marks in a 1/2 inch space without getting "out of the lines" is not likely. Yet that's what we are basically asking of them. 

Rotating their wrist up and down or laterally is equivalent to me doing a somersault. It is not going to happen with a pleasant outcome. If their movement is not smooth and refined the results are pushing too far causing a gag or poking tender tissue. 

Add to this that moving their tongues for feeding is a new and unrefined skill. Do you ever have problems keeping your tongue away from where the dentist is working? And how long have you been practicing oral motor skills? They are more skilled at biting and sucking. That's what they have had the most experience doing. 

No wonder they get frustrated and refuse to do a task that is so risky and difficult for them. My definition of toddler could be "independence seeker". Yes, it would be easier if you did the task for them, but goes against their "I'll do it myself" agenda at this age. 

The strategies listed in this post are about motivating a child to keep trying. Being aware of the difficulty of the task of toothbrushing will help you understand his resistance and discover reinforcers that are worth his effort and discomfort and gain his cooperation.
We sing the song (Ariel's theme) from Little Mermaid while we brush, the kids get a kick out of it and encourages them to open their mouths wide for the ahh-ahh-ahhs.