This is classic Klondike Solitaire, the card game most people just call Solitaire. Build the four foundation piles up from Ace to King in each suit, and stack the tableau down in alternating colors to free the cards you need. Deal from the stock whenever you run out of moves.
It plays free right in your browser with nothing to install, and works on both desktop and mobile. A familiar, relaxing game for a quick break or a long sit down.