The 3x3x3 is the classic puzzle invented in 1974 by the Hungarian professor Erno Rubik. It is the standard for speedsolving and the main event at the majority of WCA competitions. There are 43,252,003,274,489,856,000 different combinations but they can all be solved in under 7 seconds by the best in the world. If you want to start your journey in joining them this is a great place to start. The following tutorials will teach you how to solve a cube and if you want get faster:

Learn to solve:

Video Tutorial

Written Tutorial

Beginner Speedsolving:

Choosing a Speedsolving Method

Fingertrick Tutorial

Introduction to F2L

Introduction to 2 Look OLL

Introduction to 2 Look PLL