You start your turn with a "bank" of 1 Action, 1 Buy and 0 Coins. During your Action phase, you may spend 1 Action to play one Action card from your hand. If you do, then you do everything that the card says on it, in order, to the best of your ability.
If the card says "+(n) Card(s)", then you immediately draw that many cards from your draw pile. If you need to draw a card, and your draw pile is empty, then you shuffle your discards to form a new draw pile and continue drawing. If your discards are also empty, then you don't get to draw any more cards.
If the card says "+(n) Action(s)", "+(n) Buy(s)", or "+(n) Coin(s)", you add that many Actions, Buys or Coins to your "bank".
Anything else the card says, you apply that effect immediately. In the case of Oasis, that means that after drawing a card and adding one to each of your Action and Coin banks, you discard a card (if you have any cards left in hand). You may then play another Action card from your hand, if you have one.
This becomes very important when you're resolving cards via something like Throne Room. For example:
- Spend an Action to play a Throne Room
- Select Oasis to play twice
- (First play of Oasis) Draw a card
- (First play of Oasis) Add one Action to your bank
- (First play of Oasis) Add one Coin to your bank
- (First play of Oasis) Discard a card
- (Second play of Oasis) Draw a card
- (Second play of Oasis) Add one Action to your bank
- (Second play of Oasis) Add one Coin to your bank
- (Second play of Oasis) Discard a card
At this point, you now have at least two Actions left (almost as though you'd played a Village), plus two extra coins to spend in your Buy phase, and you've cycled two cards in your hand. If you have another Action card in your hand, you may spend one of your Actions to play it.