How do the different European football (soccer) leagues and championship series interrelate with each other and function?

Right, so this is an enormous question that I will attempt to handle as concisely as possible while still conveying the most information. (I became a fan of in high school but didn't really start following English (and European) football until my freshman year at , so I'm relatively new to it as well. Those who have been following it for much longer should feel free to correct/add on to this answer as necessary.) Also, TL:DR; is at the bottom. In general, the top leagues across all nations have the same general format: your team plays against each other team in the league twice (so 38 games in the , , and , 34 in the ). You get 3 points for a win, 1 point for a draw, and 0 for a loss. The team with the most points wins the league, with goal differential being the primary tiebreaker (that is, the margin between the goals your team scored and the goals your team conceded). The benefit about being in the top league in your country is that you have the chance to qualify for the , an annual competition between the champions of each nation's top league (hence the name). Here's where it gets a bit tricky, because each country has a certain number of teams that it can send to the competition, which number may change from year to year based the nation's UEFA coefficient, which is determined by how well teams from your nation have done in European competition over the past five years. For the sake of brevity, more information can (and should) be found http://en.wikipedia.org/wiki/UEFA_coefficients#Country_coefficient. For the sake of example, the top 3 countries (Spain, England, and  Germany) are allotted 4 Champions League slots and 3 Europa League  slots. The next 3 get 3 Champs League and 3 Europa League slots, and so  on. Okay, so let's take England and Italy as the two examples, since those are the two leagues the OP is most interested in. So this season, the 3 teams that finish at the top of the Barclay's Premier League gain automatic berths in the group stages of next year's Champions League. The team that finishes fourth will also play in the Champions League, but they will have to play a qualifying round before they can be assured of their place in the round-robin. In Serie A, it is the same except they have one less allotted Champs League slot, so only the top two are guaranteed the round-robin, while team 3 must play in the preliminary qualifying round. I also casually mentioned the Europa League earlier. This is a secondary European competition (think of it as the Serie B to the Champions League's Serie A) for the teams who finish just below the top 4/top 3. Again, how many teams can participate in the Europa League is determined by your nation's UEFA coefficient. England and Italy, as I mentioned, have the same number of Europa League slots for next year (3). The interesting thing about the Europa League, however, is that you can secure a spot by winning your nation's primary cup competition (the Coppa Italia in Italy, the FA Cup in England). If you win the cup and have already qualified for European competition, though, then the slot will simply fall to the next-highest finishers in the table. At the other end of the table, of course, is relegation. Almost every European country has at least two leagues of professional football, which means you're not always going to be playing the same teams every year. In general, the three teams that finish bottom-most in their league will get sent to the league below, while the three teams that finish at the top of the league below will get promoted to the league above. I'm not certain of the process in Italy, but for England, this is true all the way down to the semi-professional/amateur level (as far as I know). SO, to tend to your Napoli-Cagliari example, the reason the game was irrelevant for Cagliari but critical for Napoli is that Cagliari has nothing to play for in the league. It is highly, highly unlikely that they will obtain European qualification through league play, and they are out of the Coppa Italia, but they are also in no real danger of being relegated. For them, the season is essentially over. Napoli, however, has AC Milan nipping on their heels for that second-place position, which is the difference between automatic round-robin qualification in next year's Champions League and a preliminary two-leg qualification match. As of my answering this question, Napoli has a 7-point lead on Milan with 5 games (aka 15 points) still to be determined. So Napoli has a vested interest in not dropping any points unnecessarily. PHEW. Okay. So to recap, these are the basics of European club football: Your position in the league's table is determined by the number of points you win throughout league play. Your qualification to play in cross-national club competitions (the Champions League and the Europa League) is dependent on your final position in your national league's table (or if you won your nation's primary cup competition). The number of teams your country can send to these competitions is determined by how well your country's teams have done in those competitions in recent years.

This is a complicated question, but I'll try to give you the gist of it. Let's focus on Serie A for the moment. Serie A is the top-level league in Italy. It is played in the form of home and away fixtures between all pairs of teams, meaning each of the 20 teams plays 19 x 2 = 38 games in a season. There are no playoffs, this is true for almost all domestic top-level leagues in Europe (there are playoffs in Belgium). At the end of the season, the team at the top of the standings is crowned as Serie A champions. The bottom 3 teams are relegated to Serie B and replaced by 3 teams that move up from Serie B. The top 3 teams go to the Champions League the following season. This number varies with the country depending on how successful their clubs are in continental competition. For example, Spain, England and Germany have 4 CL spots at the moment. The next few teams (number depends on the country) qualify for the secondary continental competition, the Europa League. Both CL and EL are played alongside domestic leagues throughout the season. CL and EL games are played mid-week, domestic league games are usually played on the weekends. Every country also has a national team that is distinct from all the club teams that compete in the above competitions. A footballer must be a citizen of that country to play in the national team. International competition between national teams is totally different: games are less frequent, and major competitions such as the World Cup take place during the summer. The reason that Napoli-Cagliari game didn't mean much is that Napoli is pretty much locked in to the 2nd position in Serie A, and Cagliari is unlikely to move up from 10th but also almost guaranteed to finish above the bottom 3, so they have nothing to play for. Check the http://en.wikipedia.org/wiki/2012%E2%80%9313_Serie_A#League_table table.

Most of the Answers are really detailed, however terribly long . I just want to provide a TL;DR version. Imagine an European football team in their national league as a student in his high school classroom. Some top students would excel and compete with each other (Leauge Championship - AC Milan and Napoli) in order to be rewarded in front of the whole school (UEFA Champions Leauge & Europa Leauge). Some messes up and all that they ask for is to avoid being retained. (Relegation) Some are caught in the middle and enjoy life at their own pace, just passing courses. (Cagliari) Moral of the story is: don't get retained - if you happen to excel, you will get rewarded and glorified.