How do you normalize a table?

I've been user of Access 2003 for a while and am ok using databases but
somehow lack practical knowledge when it comes to redesigning or normalizing
existing database and hope someone can guide me step-by-step.

I'm trying to redesign our dog training club membership database.
Out membership is based on household but we have only one set of handler
name, mobile (cell) phone and email fields in our enrolment form and such was
the case with our database Member Table. Soon we noticed people putting
multiple names, mobile numbers and emails so we added second set of handler
fields in the Member table to accommodate this.

I decided to normaliise and create a new Handler table, put all surname,
first_name, mobile_no and email records acroos from Member table and link
with Member_ID as foreign key, while each record will have Handler_ID as the
primary key.

Could someone let me know how to go about from here? I'm planning to do
this at home using Access 2007, although ultimately it will have to be made
compatible with Access 2003 as that's the version used with our Club computer.

Thank you.

--
Maki @ Canberra.AU