Playing through the campaign will get you a good amount of progress towards this, but probably not enough to complete it.
You can build unnecessary bridges to nowhere during campaign missions, or just start up a sandbox game on a map with multiple islands and make bridges until it unlocks.
Building bridges is pretty easy, you just use the regular road building tool. Only tricky thing is remembering to not start the bridge too close to the shore. You need to be a couple squares away from the water to start your bridge properly.