6 leagues, all dynasty, though with various rulesets. Two 13-man keeper dynasties, one salary, one contract/salary, one contract, one deep dynasty. All are IDP except the contract/salary. I like the challenge of learning new styles of play. In fact, two of those are because I took over a last place/talent-poor dynasty team and wanted to see if I could turn its fortunes around.
I work and go to graduate school, so I fit in my hobbies around other priorities. Leading up to the NFL Draft, I tend to do the most research, setting aside a few hours a couple of times a week to just look at players and make ranking sheets, etc. I compile a lot of information into spreadsheets, and that takes several hours. Still, aside from that time of the year, I only really spend 1-2 hours a day on reading/analyzing. It’s pretty spread out throughout the day. You know; wake up, check the Web while I eat breakfast, go to work, maybe check if it’s really slow and I’m bored, then come home and check what’s going on before bed. It all adds up, but it's not really like I'm devoting time to it, and it doesn’t interfere with anything. It's no different than any other hobby. When you have downtime, you gravitate towards what you enjoy, whether it be fantasy sports research, gardening, working on cars, whatever. I enjoy fantasy sports (I'm also in a pair of dynasty baseball leagues which I've been in for about 15 years).
Still, I've found that knowledge really snowballs. It’s like anything else you learn; you just keep building on what you had before. In the last four years, I've seen my knowledge grow by leaps and bounds, particularly on the IDP side. Like anything else, first you learn the big generalities, like the Top 10 DL and the Top 10 Sleepers then you start learning about other tiers of players, then you learn WHY some players are sleepers or how schemes affect production, then you learn about next year's prospects, and before you know it...
I think the most important thing, though, is to learn how to NOT rely on other people’s judgments. Don’t just take people’s lists and rankings to heart. Learn the strategies and skills that underlie the analysis, and draw your own conclusions, then take the appropriate actions. Don’t let other people do your thinking for you. Weigh their analysis and opinions, yes, but make sure you have your own as well.
In general, I don't think the number of leagues you're in matters terribly much. After all, I use the same information-gathering tactics that I did when I only had a couple of leagues. I find there are only two significant "problems" with more leagues:
1. Confusing rulesets. I see this happen in a couple of them, where people forget what league has what rule on waiver pickups, bid amounts, IR usage, etc.
2. It's harder to keep track of what players are available on the waiver wire, which means some players can slip through the cracks.