(2) Mooch off other people's work. Websites that connect family trees (such as ancestry.com) and also just random googling off of unusual names.
(3) Look for electronic datasets. And then look again. ancestry.com collects a bunch of datasets, but I could not find my great-uncle's death record. I _could_ find it in the Washington State digital archives, as a Social Security Death Record -- but those are in ancestry.com and I couldn't find it there. There are Dutch marriage/birth/death records in ancestry.com, but it's not clear what that collection is -- it isn't everything in genlias, but it has more than genlias seems to have in some ways.
(4) That family legend? Break it down into its component parts. Be suspicious, but don't just assume it's false because there may be important clues in it that will be helpful later.
It used to be a whole lot of letter writing and typing and meticulous record keeping to do this stuff. Now, it's a whole lot of googling and electronic matching. There are probably people out there who would sniff and say the quality has gone right downhill (and in some cases, they're definitely right -- nothing else explains a father field having someone younger in it than the person they supposedly fathered. ancestry.com really tries to stop you from doing this, but people do it anyway and then other people copy it). But I'm working off of paper genealogies for part of this and they are definitely not error-free, and it's way easier to fix an error in an electronic tree than it is on typed and photocopied family group sheets.
Weirdly, I've never read a book about how to do this stuff; I sort of grew up with it. I've ordered a couple because it seems so _wrong_ not to have read a book about it, and there are still points where I'm learning obvious things very slowly. (Newspapers! Newspapers!)