I can only speak from my own experience, and I've only learned to DM once (like many people here, I suspect
). It was a very long and torterous learning experience starting with 2e in middle school, all the way through 3e, 3.5e. It wasn't until I was 23 and starting 4e that I felt I could really call myself a decent DM.
I'm not sure how much of it has to do with my age and the people I played with, but I'm going to credit the 4e DMG1 with the most significant part of my growth as a DM. The 3e DMG was filled with stat blocks and templates, and was almost completely useless to a new DM like me. The 4e one is written very well, covering all the basics in a logical way. I remember having many DM-driven questions back in 3e, like "How often should I deviate from the written page?" and the 3e DMG just doesn't cover stuff like that. The 4e DMG explains nearly everything a DM needs to know in basic terms. And the 4e DMG2 picks a couple topics in DMG1 and expands on them, delving into many interesting details of drawing characters and adventures forward.
In other words, I highly recommend picking up a copy. That said, can you DM without it? Absolutely. If your players are anything like mine, they will forgive you and still have a great time. And a lot of the questions answered in the DMG can be answered here on EnWorld or in a multitude of articles online targetted at new DMs. But I think the high quality of the writing and the availability of that much information in one place, makes it a go-to book for any problem you might run into as DM.
As for statblocks, you can get the DC table from the free erata on WotC's site. The two tables you will find most useful besides that are the treasure tables and the NPC/Encounter XP targets tables. I am fairly certain you can find those in other places. For example, the NPC XP table can be mathematically derived by using any stack of monsters. Let's say you want to figure out the target XP for a Level 5 encounter. Just find any Level 5 non-solo, non-elite NPC in the Compendium or elsewhere, and multiply the XP of that monster by 5. That's your target.
But if you're wondering how to actually *use* that information... that's in the DMG1.