Ah, the joy of mudding and taping sheetrock. In order to be successful, you must approach it with a zen-like mindset. It actually can be somewhat enjoyable and I have kind of missed doing it. The last time I was doing this was for the back bathroom. So now I am in the laundry room next to it and finally getting to doing it (uh, the drop ceilings were removed from both rooms at the same time so I've been needing to get on this for a while now).
But zen-likeness aside, there is definitely an art to mudding and taping drywall so I will quickly go over some of the key points in which to keep in mind.
1) Tools: I spent a small fortune on my knives, but worth every penny. Not only should you get good quality knives, but lots of different sizes is very important. I stay away from the blue steel kind and go straight for stainless steel (blue steel will rust and as I will point out below, mudding is all about water - lots and lots of it). I had to get some of mine online cos the local mom and pop hardware store didn't have every size I wanted (and the Big Box guys don't even carry Marshalltown which is the brand I would highly recommend).
Anyways, I have just about every conceivable size: 2" (for cleaning tools), 4" (for general prep, knocking down the last coat, and other miscellaneous tasks), 6" (for the first coat I put on after the tape is up and dry), 8" for the next coat, 10" (for applying each coat of mud - much faster with a wide knife then a narrow one when you're looking at a 12' section - and for the following coat), and 14" (for those bad seams and repair jobs where having an über-wide knife is essential). Do not underestimate the need for that many tools - a knife too wide will get you in trouble, and those really wide knives are important for seams and areas that require a wide feather. I also have a corner tool (not necessary and sometimes I do corners without it) and a ceiling tool - it's kind of a pain getting mud on it from the pan but it works really well for applying mud on the ceiling. Definitely worth it.
2) Tape: like in the photo, I only use and recommend simple ol' paper tape. It has a seam down the middle so it can be folded perfectly for corners. Do not bother with mesh or any other kind of seam tape. Oh, but I do use the mesh kind for repairing holes in walls - just not for drywall seams.
3) Mud pans: get two, one stainless and one plastic. I use the stainless for the mud (do not bother with the cheap plastic ones for mud - they are much, much harder to clean after you've finished) and the plastic just filled with water that I use to run the tape through and dip my knives.
4) Water: as I mentioned above, mudding is all about time and water. You have to be quick once you get the mud on the wall, but more importantly you need lots of water! That's why I keep a plastic mud pan full of water. I run all tape through it completely before embedding in the mud, and when I am taking off a coat I dip the knife in the water before running it down the wall. This is essential. Keep all of your knives wet!
5) Feathering: like I also mentioned above, make sure you work progressively. For novices like myself, I first apply the tape and, once it's dry, then apply the real, first coat. Pros combine this step but a pro I most certainly am not. But when you put on the tape, only use just enough mud to embed it and create a tight seal (very important!) with the wall. No extra mud. Then the first real coat is applied with the 10" knife horizontally across the tape just as wide as the tape because it will be taken off with only a 6" knife. You do not want a wide feather for this first coat. Each successive coat is then applied slightly wider than the last - I typically do three coats.
6) Mud: I use a 5-gallon bucket of just standard mud for everything but the last coat. The last coat I use a topping compound which is lighter (finer might be a better word to describe it) than standard mud and easier to sand.
7) Sanding: never sand until you are finished putting on all coats. You do not want to sand in between coats! That is a waste of time and you should be putting on the mud and taking it off with the knives good enough to not have to be sanded in between coats.
And I realized sanding mud is just like feathering a mask in Photoshop - the softer the better (i.e. a soft edge obviously will not show once the walls are painted). If you can feel the edge, sand some more because it will show. Nice feathers are key to never seeing the seams.
8) Inspecting: use a 500W halogen lamp and shine it at an angle at the wall. Every conceivable defect will show. It's your call then to decide just how perfect you want your walls.
Hmm, I think that's about the gist of it. Good times. Now back to work.