Each network has its own procedures. You would do best to find the network's website for step by step info for them. Some networks don't have registration services, others, like DALnet do.
Some channels are set to only allow registered and identified nicks to join them. To find out if the nickname you want is available, in any window type: /nickserv info nickname
To learn how to register type /nickserv help register and look in your status window for instructions. DALnet has also set up a web site with helpful documents on this and many other subjects. See http://help.dal.net/docs/
Remember that passwords are case sensitive, and chicken is not the same as CHICKEN or cHiCKeN. Nick registrations are two step, the second part is to enter the authorization code you will recieve in an email from DALnet. That only needs to be done once. You must identify to your nickname within each specified period of time in order to keep it registered. While it is usually 30 days, due to current problems it is temporarily 60 days. To be safe, anything involving a password should be done in your status window in case of typos. To identify you simply type /identify yourpasswordhere.
To learn how to register a channel, type /chanserv help register
If you need help with any DALnet services commands, besides going to the website mentioned, you can always type /nickserv help or /chanserv help followed by what you want to do, ie:
/chanserv help set
/nickserv help set
Write your passwords down in a safe place, but if the dog eats the paper:
To have your nickname password sent to you, use:
/nickserv sendpass Password EmailAddress
To have your channel password sent to you, use:
/chanserv sendpass #channel Founder's EmailAddress