Try to expose every square in the grid that is not one of the hidden mines, without opening any square that is a mine.
Every opened square is marked with the number of mines in the surrounding 8 squares, if there are any; if not, all the surrounding squares are automatically opened.
The first square you open is guaranteed to be safe, and you are guaranteed to be able to solve the whole grid by deduction rather than guesswork.
On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click).
Click a square to open it, or, on a numbered square with exactly the right number of flags around it, open all the squares around it that are not flagged. Right-click it to place or remove a flag, if you think it is a mine. Keep the right button down and drag to do the same to every square you pass over that looked the same as the first.
With the keyboard, the arrow keys move a cursor around the board. Enter does what a click does to the square under it, and Space what a right-click does.
Check & save checks your flags against the mines, as it checks your answers in every other puzzle, and highlights a flag on a square with no mine under it.
The mines are laid out around the first square you open. If you undo that first move, the board is not laid out any more: whichever square you open next is safe in the same way, and gets a board of its own.
If a grid seems to need a guess, look again: there is a deduction to find, perhaps one about the total number of mines. Every report since the game was written in 2005 of a grid with two solutions, or one that needed a guess at a safe square, has turned out to be a deduction missed rather than a fault in how the grid was made.
Hint explains the next step rather than simply making it. Each step flags squares that must be mines or opens squares that must be safe. It waits until no flag is wrong, as Check & save does. The hint reasons only from the numbers you have opened, never from your flags, since a flag may be a lucky guess until the numbers prove a mine under it: a mine it mentions is one the numbers prove, and flagged by an earlier step if you had not flagged it already. An unopened square, in its words, is one that is neither opened nor proved.
A few ideas are worth learning by name:
The first step of a new board opens a square in the middle: no mine is ever laid in the first square you open or beside it.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.
20% of the grid's squares. There must be at least nine squares without a mine, because none is ever placed in or next to the first square you open. It must be at least 1.