Once you have the card you want to use in your hand, check its cost. You'll see the Mana cost in the Mana Crystal on the card's top left.
If you have enough Mana, just drag and drop the card towards any empty space around the middle of the battlefield.
If you have played a Unit, it will then fly and materialize automatically in its adequate spot, depending on the presence of Keywords such as Stealth (Stealthed Units go to the left of your Hero) or Guard (Guards are always positioned to the right of your Hero). If the Unit has no Keywords relevant to positioning, they will march to the left of your Hero. Mootichi, in the example below, will sneak towards the left of your hero, trying to remain inconspicuous while using its powerful abilities.
If the card was a Spell, it will fly towards the screen and immediately invoke its effects over the battlefield. Then, its power spent, it will go to your Grave.