Does Tor encrypt a client's connection to its entry node? How does it do this?
Yes, Tor clients encrypt connections to entry nodes (relays). Indeed, they successively encrypt to all relays in the circuits that they specify. The required public keys for all relays are available from Tor's directory servers.
Does Tor encrypt a client's connection to its entry node?
Yes, it does. You may look at Pabouk comment for a degree of an explanation of this subject.
How does it do this?- Not sure what you want to hear here. An explanation where in the source code it does it or what methods/cipher are used? In any case. That would be a separate questions. Please edit your question.