An example of an american voter registration form can be viewed at http://www.spotsylvania.va.us/emplibrary/VirginiaVoterRegistrationApplication.pdf
The onus is on the individual voter to register - there is no legal obligation to do so - and a major part of the work of party campaigners and others this year has been to persuade people to register. When I was in Maryland during the 2006 election I visited a university campus and there were a number of voter registration stalls set up for students to register, including one by the main bus stop.
In the United Kingdom a form is sent to each household once a year, and this form must be completed and returned (failure to do so can lead to a fine - though I've never heard of this happening). Councils should make every effort to chase up unreturned forms and actively seek to promote registration. However, particularly in areas where there are high turnovers of population - full registration is never achieved.
A website allows British citizens to register: http://www.aboutmyvote.co.uk/how_do_i_vote/registering_to_vote.aspx