Steps
Cross
This first stage involves solving the four edge pieces in one outer layer of the puzzle, centering around a commonly coloured centre piece. Many speedcubers usually solve the cross on the bottom side to avoid cube rotations, which slow down solve times.
F2L
In First Two Layers (F2L), corner and edge pieces are paired up and later moved to their correct location. There are 42 standard cases for each corner-edge pair including the case where it is already solved. It can also be done intuitively.
OLL
This stage involves manipulating the top layer so that all the pieces therein have the same colour on top, at the expense of incorrect colours on other sides. This stage involves a total of 57 algorithms. A simpler version, called "two-look OLL" orients edges first and corners afterwards. Algorithms are usually performed two to three times for this version. It uses ten algorithms, three for edge orientation and seven for corner orientation.
PLL
The final stage involves moving the pieces of the top layer while preserving their orientation. There is a total of 21 algorithms for this stage. They are distinguished by letter names, usually based on what they look like with arrows representing what pieces are swapped around (e.g., A permutation, F permutation, T permutation, etc.). "Two-look" PLL solves the corners first and edges separately. It uses six algorithms, two for corner permutation and up to four for edge permutation. Also, a U-perm can be repeated if the user wishes to use even fewer algorithms at the expense of usually faster solve times.