I’ve seen many questions asked about the rules of qualification to the European Cups, on this, and on other forums. There seems to be a lot of assumptions and uncertainty in people’s knowledge about the subject so I thought I’d write a short résumé to clear things up. Here it goes…
All countries and teams in Europe are ranked in what is called the UEFA coefficient.
England is awarded a certain number of spots in each of the European cups. The amount of spots is determined by England’s placement in the UEFA coefficient. The results from the two main European club competitions earn points for each club playing and the countries those clubs belong to.
The points earned by all the clubs from a country are added together and divided by the number of clubs participating from that country, to give a figure called the country coefficient. The country coefficients of the five last completed seasons are added together, and the member countries of UEFA are then ranked in order, highest figure top.
According to what place a country has in the country ranking, it is entitled to a particular number of places in the Champions League and in the UEFA Cup. UEFA also assigns the stage at which a country's teams start in each competition from this ranking.
Each team has a separate ranking in the Club Coefficient. This determines their place in the seeding's of each competition.
No country can be awarded more than 4 places in any of the European cups. This is a relatively new rule which was created after Liverpool winning the Champions League in the 04/05-season, whilst missing out on next year’s competition by only managing 5th place in the league. This led to the UEFA-resolution that all winners of the European Cups will be automatically qualified for next years tournament as defending champions. Should they not qualify through their own national competitions; their spot will be awarded at the expense of the lowest qualified team from their own country.
(As a digression I should mention that in the season following Liverpool’s “achievement”, as it had never happened before, the UEFA made an exception to that rule. So for the 05/06 season, England was awarded 5 spots in the CL, avoiding the exclusion of the 4th placed team in the Premier League. But how sweet wouldn’t that have been after Lasagna-gate?)
Next season, England will be awarded 4 spots in the Champions League and 3 spots in the UEFA-cup. This is the most number of places a nation can be awarded based on the UEFA Country Ranking. As per today, only two other countries are awarded as many places, they are Spain and Italy.
These spots are divided as follows (as decided by the FA):
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The 4 Champions League spots are awarded to the 4 top placed teams of the domestic league.
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1 spot in the UEFA-cup is awarded to the 5th placed team of the domestic league.
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1 spot in the UEFA-cup is awarded to the winner or losing finalist of the FA Cup.
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1 spot in the UEFA-cup is awarded to the winner of the Carling Cup.
If the winner of the FA Cup qualifies for any of the European Cups through their placement in the Premier League, the Euro-spot goes to the losing finalist.
However…
If the winner of the Carling Cup qualifies for any of the European Cups through their placement in the Premier League, the Euro-spot goes to the best placed team in the Premier League that has not already qualified.
(So if Chel$ki wins the Carling Cup this year, the spot will go to the 6th/7th place in the Premier League depending on the finalists of the FA-cup)
So that’s it. Hope I’ve cleared things up a bit for you. At least I learned something whilst researching it 
If you whish to learn more on the subject, here are a few links to related material:
UEFA European Cup Football - results and qualification - by Bert Kassies – this is simply the best place to go for information on this subject.
Current Country Ranking (including preliminary points for this season)
UEFA Country Coefficients (points) for 2007/2008
UEFA Team Ranking 2008
Wikipedia UEFA Coefficients and UEFA Wiki