Stake deposit is automatically taken from your wallet.
When you begin delegating, it takes 4 epochs to get your first rewards. Here’s why:
The Cardano protocol takes a snapshot of your Ada balance and pool choice at the beginning of each epoch, then apply that in the next epoch.
Epoch 0: You start staking with your pool of choice.
Epoch 1: The Cardano protocol remembers your Ada balance and pool choice at the beginning of this epoch .
For example: 10,000 Ada, RATS pool.
Epoch 2: The Cardano protocol begins staking 10,000 Ada with RATS pool.
Epoch 3: Your rewards is calculated.
Epoch 4: Your rewards is paid to you.
Rewards calculations and payments are done automatically by the Cardano protocol.
Later if you switch pool, you will still get rewards from the previous pool for the next 3 epoch before getting rewards from the new pool.
Hope that helps.