Bicycles are rather useless in the city center (however you can rent bikes and they're lots of fun, but usually are used only in the parks). Many locals ride scooters to work and for shopping.
Prague has many bicycle paths (even dirt bike tracks), and there are a variety of Bicycles that are available to rent for tourists (including electic bicycles and scooters). Prague used to have public bicycle rentals (similar to carts at the grocery) - but the gypsies stole all the bikes on the first day.
The best place for riding bikes in Prague are the park paths, and paths along the river. You can ride a bicycle in the streets, following generally the same laws as you would in a car. You should not ride a bicycle on sidewalks, unless you're in a parks area. The Czech Cycling Federation or CSC (in Czech: Český Svaz Cyklistiky) is the national governing body of cycle racing in the Czech Republic.
Perhaps the coolest bicycle that can be rented in Prague, is a giant platform (similar to a hayride) with kegs of beer on tap, and pedals for everyone sitting at the table to power the vehicle around the streets of Prague.
FYI the Czechs like to buy matching outfits for each of their activities - so the guys wearing helmets and lycra racing outfits are less likely to be professional bikers, and more likely to be amateurs or hobbyists who really don't know much about bikes.
The Brno is a velodrome in Brno, Czech Republic. It is a 400 m outdoor covered concrete velodrome with an underpass and lights. The velodrome hosted the 1969 UCI Track Cycling World Championships and 1981 UCI Track Cycling World Championships. The velodrome still has the 1969 look and serves to bicycles club TJ Favorit Brno and it is a site for hosting various concerts and performances. As of 2015 there are still international cycle races taking place.