Splinterlands is a one on one, skill-based battling game. If you want to battle against another player, you can click the "Battle!" menu option at the top of the screen and then choose the Ranked or Practice battle options. Playing Ranked battles will allow you to increase your rating as you win and reach higher leagues to earn increasing amounts of rewards at the end of the season. When you are just starting out and are below 100 rating, you will not lose any rating points for a loss in ranked play, so there is no downside to playing ranked battles even when you're just starting out.
Once you have chosen the type of battle you would like, you will be matched up with an opponent of similar rating, and you will be given a randomly chosen set of battle parameters. You will both then have a limited amount of time to create a "team" of cards, consisting of one Summoner card and between one and six Monster cards based on the given battle parameters. Once each player has chosen their team, the battle will begin and will play out automatically based on the predefined game rules, and the first team to destroy all of the Monsters on the opposing team is the winner! It is also possible for battles to end in a draw.