Do I have to send you my tokens to stake with you?

No. Your tokens are never under the control of the node you stake to, and never leave your wallet.

Delegating to a validator node, simply put, is putting your tokens (XRD) into a special staking ‘state’ within your own wallet. While they are in this state you are unable to do anything with them, but they can be unstaked at any time.

Please remember there will be a delay when unstaking (approximately 2 weeks). The purpose of this delay is to allow the network sufficient time to determine confidently that the validator those tokens were delegated to hasn’t done anything malicious - no need to worry though, this is a totally normal procedure in DPoS networks.