In attempting to upgrade from DL1 today, I went into the Library/Licensor screen and selected Buy New License, thinking that would upgrade, but it didn't. So, I downloaded DL2, it converted my DL1 library (into a new database file leaving DL1 alone), and then I tried the Buy New License option again, this time it worked and registered my copy.
Of course, the DL1 new license I purchased cost $20, then I had to select the Upgrade price (another $20) in DL2 when I tried the second time. To be fair, when I purchased the DL2 upgrade the second time, it said that if I had purchased DL1 within its free upgrade window, I wouldn't be charged for the upgrade (even though I had to go through with the credit card info again). I sent an email off to Delicious Monster to see exactly what I was charged, just to see if I have to do anything more not to be billed twice.
Anyway, to answer your question, the easiest, most direct way to upgrade is to download DL2, and after it starts up the first time and converts your DL1 library, go to the Library/Licensor area, select Buy License, select the upgrade option, and pay for it. As I said above, if you appear in their database, you're not supposed to be charged again for the upgrade, even though you have to enter your credit card info again. We'll see if it works.