To challenge other players, go to the Battle screen from the top row of icons. You'll notice a big green tutorial button - tap or click the arrows to switch to practice or ranked matches.
Each battle begins with a small pop-up window with information about your opponent, the mana limit, and special conditions. The conditions can be anything from limiting both teams to a certain Splinter or prohibiting flying monsters from fighting.
Splinterlands first finds you an opponent and sets the rules of battle. These rules will always change from battle to battle.
Next, you will need to choose a formation for your team. Think of it as your positions in linear order. Position 1 can only be occupied by monsters with melee damage (unless their ability allows them to perform ranged or magic attacks). All other positions are reserved for ranged and magic attacks, again, unless your Monster's abilities avoid this rule.
If you find acceptable conditions, proceed to form a team. Remember, you only have two minutes for it. Pay attention to the Attributes of the cards and try to compensate for your weak points with the Summoner card.
Key takeaways:
Don't rush into head-to-head ranked battles. Complete at least a couple dozen practices to make sure you really master the game and are interested in your current deck.
Make use of your starting position. As long as you remain below a grade 100, you will not suffer a grade penalty for losing. This is the perfect time to get more cards and experiment.
Study your letters in advance. You will never have enough time to study them after agreeing to the battle conditions. It would also help create some sort of presets for various Mana limits or conditions. Your main objective is to build a team that is diverse in its Abilities where each card strengthens each other. For example, a taunt ability tank card works well with ranged attack or magic cards with high damage and low health.
Look for missions! Quests are a great way to get loot more often. Most of these work the same way as conditions, prompting you to win battles with a particular Splinter or something similar.