What are the common skewb methods and pros and cons of each?
The four most common skewb methods:
The Kirjava-Meep method (aka "Kirmeep")
Pros: Fully developed; algs are useful for other methods as well. Notation is consistent with WCA notation, except "D" is used in place of "B".
Cons: Some people find FCN algs to be slower for their hands.
Meep has averaged around 6 seconds with this.
Sarah Strong's Method
Pros: Low alg count (2 algs, and they're inverses of each other! Same alg as the 1-alg method). Very easy to finger trick.
Cons: Gripping the puzzle as Sarah does can be difficult to understand for beginners.
Sarah has averaged sub-7 iirc.
Ranzha's Skewb Method
Pros: Primarily based on intuition, many algs are short and join up to create new ones, easy to "hack".
Cons: Layer stays on U, and thus recog can be difficult to get accustomed to. Many feel turning style is awkward.
Ranzha (aka me) averages around 6.
The 1-alg method (popularized by Chris Bird)
Pros: One four-move algorithm that's easy to finger trick.
Cons: Inefficient; as a beginner's method, it does the job.
Mitch Lane has averaged sub-10 with this.
I really don't advise learning the 1-alg method because it's slow, inefficient, and it doesn't take much effort to learn one of the other three methods.
Sarah and I have made video tutorials for beginners as well:
Sarah's:
http://www.youtube.com/watch?v=qpykCxeMA6U
Mine:
http://bit.ly/ranzhaskewb
There's more that can be said about each of these methods. If you're going for a legit speedsolving method, of these, Sarah's is most widely used. It's important to delve into each of the techniques of each method, for versatility's sake. Also, it's important to explore on your own because, who knows, you might find your own great method!