Voting in British elections is simpler than in the USA. For one thing there are no registration drives before an election - every household is sent a form annually - which must be filled in, on pain of a fine (I sent mine in yesterday). It is the responsibility of the local authority to ensure that the 'electoral register' is as complete as possible. Having said that there are concerns about the number of people who, for one reason or another, are not on the register.
Elections are less complex. British voters generally one have one election at a time - the election of their MP, or for the district council, or the county council. In the last three General Elections there have been County Councils elections on the same day - so many voters will have had to complete two ballot papers (each vote for an elected position requires a separate ballot paper). Some people even had three or four ballot papers to fill in - if there was a district by-election (special election in US parlance) and/or a contested parish council election. That's the most complex it can get. No list of different positions to be filled, so no need for voting machines to punch holes!
In Britain a candidate is voted for by placing an 'X' next to that persons name (there are now some elections where a proportional or other variant system requires placing numbers by candidates names to signify preference). With the exception of some rare pilot trials, you vote by writing on a piece of paper.
Information about the process and rules of elections in the UK can be found at http://www.electoralcommission.org.uk/
Electronic voting - the subject of controvery in the US - see the recent blogs on H.R.811 - is also under discussion in the UK. The Hansard Society has its 3rd e-Democracy Conference on November 8th. One of the workshops is entitled "Electronic voting: an unnecessary risk?"
Details of the conference can be found at http://www.headstar-events.com/edemocracy07/programme.php