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: 
Having your teeth brushed by someone else isn't nice. It's invasive. Realizing that much is a good start. The right brushes, being aware of when and where your child is teething and gentleness all help, but it's unlikely to ever be an entirely enjoyable process.

The usual combination of patience, consistency and self control comes into play too.

Getting around this normally boils down to finding some way "make it fun" - in some way that capture's your child's imagination. For us, we had a few different soft toys who would "brush" my daughter's teeth, and she would choose a different one each night.
I have three children and each was a different experience in getting them to consistently brush their teeth. My oldest is 11 and unfortunately we were not very consistent with her as a youngster. She never wanted to brush her teeth. She brushes her teeth on her own now, but only because of what we did with the younger ones. My two youngest are 6 and 4. We made a conscious effort to display that both mom and dad brush their teeth every morning and night, and even after meals by making a big show of it while they were toddlers and barely had teeth. By the time they got a full set they were begging to do their own. As they got older we stayed consistent modeling the behavior and making it obvious. This in turn has helped my oldest also begin to make brushing at least twice a day a habit. My point: show your child(ren) the behavior you want them to have. Be consistent and have patience.