Thanks Wiggin! I still don't get the biggest point though, why there are two different leagues, which is apparently not geography based. And correct me if I'm wrong, that's the same in football. The way Timbuk says sounds logical, about the geography bit.. Except that's not what happens.

Btw, this is where I gave up on the wiki:

Each team plays 19 games against each of its four divisional opponents. It plays one home series and one away series, amounting to 6 or 7 games, against the 10 other teams in its league. A team also plays one of the divisions in the other league, rotating each year, with two opponents in a 3-game home series, two in a 3-game away series, and one with four games split between home and away. Furthermore, each team has an interleague "natural rival" (in many cases its counterpart in the same metro area) with which it plays 2 home games and 2 away games each year.

With an odd number of teams in each league (15), it is necessary to have two teams participate in interleague play for most days in the season, except when two or more teams have a day off. Each team plays 20 interleague games throughout the season, usually with just one interleague game per day, but for one weekend in late May all teams will participate in an interleague series.
Most of the Champions league / Euro league stuff is pretty straightforward - all European national associations are ranked based on performance in European matches over the past 5 years. Depending on your ranking, a number of teams qualifies for each competition, and at what stage the teams enter, e.g. the dutch league champion is entered straight in the group stages, and the runnerup qualifies for the third qualifying round. A country's league winner always qualifies for champions league, the cup winner always for euro league. Losers in the later qualifying rounds/playoffs of the CL enter the next round in the EL. Then when enough teams are eliminated, everyone is put in groups of 4, play a double round robin, and the best two teams from each group play elimination with away and return matches until there's a winner. The whole champions route simply means a league champion can only play other league champions in the qualifying round to prevent top countries dominating (the English #4 is probably better than, say, the Czech league champion).

Only the ranking is a bit confusing, you basically get points for winning matches and reaching certain stages, and it's divided by the total number of teams your country had playing European that year. But for example we had an extra EL ticket this year because we won the fair play ranking, but that ticket had to go to the best fair-play-ranked team not already qualified, which had actually been relegated. So we had a second league team in the EL who of course went out in the first round, but since points are divided by the number of teams, winning the fair play ranking actually might cost us for the next 5 years (though we prefer blaming Ajax's abysmal performance this year).

Distances can definitely be vast, my home team played in Moscow last week on Wednesday, amsterdam on Sunday. But these matches are every other week, and half of them are home, and the other two away matches are much closer (Manchester and Wolfsburg, although they are of course all far away for CSKA Moscow.