I am not able to figure out how to get lava. read the quest more than once.
Make a crucible out of porcelain clay (clay + bonemeal). Cook the crucible in a furnace. Make a coal block. Put the crucible on top of the coal block and right click to add cobblestone into the crucible. Add more cobblestone as it melts down. Once there is 1000mb of lava in the crucible use the bucket to get it out. Replace the coal block underneath the crucible with the lava.
You can also put the crucible on top of a furnace. It will melt cobblestone while the furnace is cooking something. Some things melt lava faster than others.
Awesomite Block>lava>coal block>furnace
Eventually with transfer pipes, multiple crucibles, stone barrels and transfer nodes you can automatically make cobblestone, obsidian, endstone and nether rack.