Don't give out your private key to anyone if you don't want to.
Your private key lets you access your account and send money. Just ask for their Bitcoin wallet address and then send the money to it, simple as that.
Fixed that for you
... With the possible exception of giving your keys to your children or being robbed at gunpoint, you should never ever give away your private keys to anybody.
It's not really your account your accessing, in very simple terms, your private key lets you sign transactions.
If you give away your private key, somebody else can generate transactions spending your inputs, and sign these transactions using your private key.
Since those transactions would be signed using your private key, the network would conclude the transactions were valid, so miners would include them into a block, and there would be no way to recuperate these inputs.