Cells on the grid can have either nothing (blank), a number (one or more mines are adjacent to the cell, or a bomb (ends the game if you dig it). Digging a cell reveals its contents.
At first you randomly tap one or more places on the screen to dig them out. You're hoping to tap spots which have no mines at all, and if you're lucky, you'll tap a blank area, which will reveal all adjacent (touching) blank areas. All of the spots next to the blank areas will have their numbers revealed, too.
Once you have at least one number revealed (Preferably more), you can use those numbers to figure out whether the adjacent cells have mines or not. The number on a cell tells you how many adjacent cells have mines. So a 1 means that only one touching cell has a mine and the other 7 touching cells are safe to dig.
Whenever you figure out where a mine is located, you plant a flag on it. Once you have revealed every cell that does not hold a mine (by digging them), you win the level.
I'm leaving a lot out... Here's a tutorial link:
http://www.squidoo.com/minesweeper