Prince of Persia is limited to 1 hour to finish the whole game and provides auto-saves at the end of each level. You may continue as many times as possible, but the total time does not reset. The game is over if the total time runs out. (In some versions you may complete the game, but the princess will be nowhere to find, resulting in a bad end.)
To complete each level you need to proceed through the gates in sequence while killing enemy guards, in order to open the final gate with stairs leading up to the next level.
In some of the versions, there is a "Validate" area after clearing Level 1, where you must read a certain page of instruction booklet, find the correct info, and drink the corresponding potion to proceed. The game is over if you drink the wrong potion (i.e. you are not playing a valid copy of the game).