There are two ways to jump in:
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(the best way) Get a client such as XChat, irssi (terminal only), or mIRC, then connect to freenode.net, then /join #arduino
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(the easy way) Use this link to connect via freenode's online gateway webchat.freenode.net/?channels=arduino
For reference: IRC does not require a sign up, though, you may wish to do so to keep sole ownership on your nick, otherwise it's a case of first-come-first-served. You can do this by logging in as normal, then "/msg NickServ help register". Also, "/join #freenode" for network help.
Channels are not recorded by freenode, it is up to the channels to decide whether they are logged or not. There is no official logging on #arduino, however, many people (myself included) keep personal logs for our own reference. There may also be bots equivalent to a google crawler which join channels, note the topic-text, and log discussion for archives and search engines.