In the version I played (2.1), you simply had the obsidian provided in a chest on the desert island (NOTE: You only need 10 obsidian for the cheap nether portal). In 1.0 or 1.1, it is impossible to go to the nether. A problem I did encounter, however, is lighting it, as you don't have any iron or flint to make flint & steel, you have no blaze powder to craft into fireballs, what are you supposed to do? Wait until lightning strikes it? That would be gay...
If you really, really, REALLY want diamonds, I have seen Captain Sparklez going to the main land by building a cobble path, so I guess it will still be possible. Just go to the world, find the diamonds, and then come back to the island.
But in my opinion, that breaks the concept of a skyblock map. You should only use what they let you use, in my opinion.
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Juega las cartas que te da el momento. Mañana es solo un adverbio de tiempo.