The first step towards Copenhagenizing a city is, of course, investment in bike infrastructure. Trying to encourage people to ride their bikes but not providing them with the necessary infrastructure serves little purpose, in my eyes.
In countries that have yet to develop a bike culture the cyclists on the roads are primarily lycra-clad males from an inaccessible sub-culture. I'm sure there are people out there for whom this is a fetish, but for car drivers who harbour thoughts about riding their bikes to work or school it is a stumbling block. In their eyes riding their bike means having to integrate into a closed sub-culture of hard-core bike 'enthusiasts'. In the process they see that they will have to invest in 'fancy' gear and 'cool' bikes. Their old three speed city bike won't suffice.
In order to encourage more people to ride it is essential to make it look easy. You don't need lycra. You don't need fancy shoes, shorts, bikes. You only need two hands, two feet and two wheels.
Just look to the Danes and the Dutch or any other Northern European country for inspiration. You don't HAVE to look like the Lycra Boys. You have clothes in your closet. Wear them. Get sweaty easy? Ride slower.
This cool cat would surely look ridiculous in the lycra outfits you see on the streets of North American cities.
No need to look like a sports freak on your way to work.
Copenhageners in their natural environment and their natural clothes.