Happy hunting!
GENERAL GENEALOGY HOW-TO ARTICLES AND TIPS:
LDS Family History Library "How Do I Begin?"
(this site also includes free forms and TONS of excellent, free resources)
http://www.familysearch.org/eng/Home/Welcome/frameset_information.asp
About.com collection of articles on starting genealogy research
http://genealogy.about.com/library/onestop/bl_beginner.htm
Free online tutorial course on online genealogy research
http://www.learnwebskills.com/
RESOURCES AND STUFF
Selection of free family tree pdf's to download - one for kids, classic box chart, tree graphic chart, etc.
http://www.misbach.org/pdfcharts/
Free family tree website - post online:
http://www.familytreeguide.com/
Free download forms and charts for organizing research
http://www.familytreemagazine.com/forms/download.html
LDS Family History Library online -
This is the BEST place I've ever gone for genealogy stuff - I've been there in person and it's AMAZING and it's free. Here's their online site, stuffed with resources from the US and other countries. There's a page on Wales with parish and family records, etc; pages on every state in the US, Canada, England, Australia, New Zealand, you name it.
http://www.familysearch.org/eng/default.asp
US GEN WEB
This is a volunteer project to provide free resources on the internet and it's got material from all over the US, organized by state and can include military records, birth and death, many other resources -
http://usgenweb.org/index.shtml
RootsWeb
Contributor-based Ancestry.com community, includes how-to articles and links to databases and many other resources - huge and overwhelming, best to go in with some idea of what you want already
http://www.rootsweb.ancestry.com/
Footnote
Some offbeat and free resources
http://www.footnote.com/
World Vital Records
Some free, some paid resources
http://www.worldvitalrecords.com/default.aspx
KIndred Trails
multi-nation resources
http://www.kindredtrails.com/index.html
Genealogy Bank
US records and newspapers from 1690 to the present
http://www.genealogybank.com/gbnk/keyword.html
US National Archives genealogy resources
Census records, military service records, immigration records, land grants, passport applications and much more - has a video tutorial on how to begin research
http://www.archives.gov/genealogy/
US Library of Congress
The link below is their genealogy reading room page but they also have online subscription service, American Memory (a digital collection of US historic documents) and tons of amazing things like interviews with survivors of the US slave era done in the early 1930s. TONS of stuff.
http://www.loc.gov/rr/genealogy/
Library and Archives of CANADA
Looks like a great and well organized site with how to's, military records, birth and death, immigration, tons of stuff
http://collectionscanada.ca/genealogy/index-e.html
Automated Genealogy CANADA
automated indexes
http://automatedgenealogy.com/
Wales Genealogy forum
http://genforum.genealogy.com/wales/
Welsh genealogy links
http://www.ukgenealogy.co.uk/wales.htm
North Wales genealogy links
http://www.northwalesindex.co.uk/pages/64.html
OGRE Project WALES
Free online genealogy search engine
http://www.cefnpennar.com/index.htm
and then there's always ancestry.com, which I don't know anything about as it's paid