Certificate Authority anyone?

I'm trying to get my head around how the CA works without much joy.

I'm assuming the CA is an application running on a server which all routers can access.

What i've learned so far is as follows:

1)The client creates a public and private key, do these keys have any significance to each other at this point or are they just random keys?
2) The client sends an unsigned cert to the CA containing a client id and the public key it just created.
3) The CA computes a hash code and encrypts the unsigned cert using the CAs private key.The result of the hash and encryption is the signiture and is attached to the cert and thus a signed cert is send back to the client.
4)The CA also sends its own cert to the client, this cert the CA sends what
important info does it contain? only the CAs public key?
5)The client now has a signed digital cert it can send to any peer.If a peer wants to decrypt the signature it uses CAs public key.

Now i'm definitely missing something here!
Firstly how does the peer get the CAs public key? Is the CAs public key unique for each peer or different?Since the data was originally encrypted usings CAs private key how can a host use the public key to decrypt, also how does the peer know what type of hashing that CA used?

Thanks in advance, i hope someone understands my questions.