Methods, links, advantages, disadvantages (mainly algorithms)
Roux method
Advantages : Very finger friendly, using mostly R U L and M turns (including wide turns)
Disadvantages : Difficult recognition for cmll, block building can be hard to learn
http://grrroux.free.fr/method/Intro.html
Petrus method
Advantages : can be very fast and easy to advance with, multiple last layer methods, such as oll pll and orient edges, coll epll, zbf2l coll epll
Disadvantages : block building is hard to learn to do, regardless of the last layer system you choose there are many algorithms. (though this applies to most methods)
http://lar5.com/cube/
CFOP (Fridrich Method) :
Advantages : Can be very finger friendly (possibly the most finger friendly of any method) Many many sites and videos to choose to learn from, Most common method at the moment so its easy to get help
Disadvantages : high move count, lots of algorithms (like 68, better than zb though), f2l can be rediculously hard to learn at first (the equivalent of block building), a Cross on bottom to limit moves, beginners can get lost doing cross + f2l on the bottom, building and destroying parts of the cube to move from step to step.
Links : pretty much everywhere, go to the speedsolving wiki if you want, for
f2l algs opticubes.com
ZZ method :
Advantages : very finger friendly at times, not too many algorithms to learn very fast
Disadvantages : eoline can be a hard step (for me anyway but maybe im just stupid), identification needs to be practiced to get good, not many tutorials that arent in polish.
ZB Method
Advantages : if you can manage to learn the rediculous amounts of algorithms and what not, its one of the fastest (maybe THE fastest) methods, however I dont think anyone knows all the cases (mirrors reflections reverses etc) as of now.
Disadvantages : Sooooo many algorithms to learn, unless you can instantly mirror reflect and reverse in your head (but I dont think anyone can do that) rather slow recognition, not all the algorithms are finger friendly so you may need to find your own
Links : Im not sure, ask Jaon Baum
VH : watered down version of zb, not much to say about it just look at zb and think, oh this isnt as bad, replaces zbll with coll and epll
If theres any other methods that im not mentioning im sure youll find them later on. Good luck