You get the mana from the card itself, and you just remember that you have it for now.
I suspect you may be confusing lands with mana and thinking that this card gives you a forest card. They're different concepts completely. This is a common way for new players to get confused.
Mana is a currency that goes up and down during your turn. Lands, and creatures like Heart Warden, are ways to get this currency. Forests, for example, implicitly have exactly the same ability, and in fact that ability used to be written on the card:
Nowadays forests just have the symbol for green mana instead, but it means the same thing:
Forests give you green mana. Llanowar Elves will also give you green mana. To cast a spell that requires 3 mana, you can tap 2 forests and 1 Llanowar Elves to get 3 mana, then spend that 3 mana to cast the spell.
For more information on this, I suggest you read the Magic 2015 Quickstart Rules, page 4 on Lands.
There are no mana cards. There are Land cards which produce mana, and there are other types of cards, like the two you mention in your question, which also can add mana to your mana pool. Your mana pool is simply the amount of mana you have available at that moment to use. When your turn ends, it goes away.
When you tap a creature like Llanowar Elves, it adds one green mana to your mana pool just like tapping a Forest card would. You do not need an extra Forest card, nor does it imply that you add a Forest card to your available lands.