-- Free resources --

Resources available to you: 

*Note: In finding out your background the end goal is usually trying to reach as far back as you can to connect with your heritage. But don't get so caught up that you jump to conclusions. Try and link at least 3 facts to make sure the individual/record is the correct one.

familysearch.org (100 %  free and many images are available. Searching for something specific like choosing a collection from this page usually is a good idea - many countries are available)

• For instance for United States searchers: 
• Try the Social Security Death Index for the years (1962 to 2011) 
• Or try the 1940 Census for anyone born before 1940 within reason

• I would suggest going here to set up an account with them because it will open up features to you not available otherwise. Such as:
• Seeing more pictures of documents than those without accounts
• The ability to save every record of importance you find to your accounts Source Box (which has features for you to organize them in folders, and create your own sources to help you sort through what is proven and what is not)
• The ability to index records as a volunteer (900 points indexing gives you a premier account with familysearch). FamilySearch Indexing is transcribing documents so they can be searched online.
• access to an upcoming public family pedigree online feature named Family Tree (already available to some presumably premier accounts try it out here note you must click the activation link). Notice that this is different from the already released new.familysearch.org tree feature.
• And all of these things 

ancestry.com

• By The Way! You can get access to ancestry.com's records for free by going to your nearest Family History Library find the closest one by clicking here (Note: If you live near a BYU campus their wireless acts like a family history library - so try it out)
• Ancestry really does have a ton of records and images to match so this is a useful site.

google.com 

• I can't stress this enough. There are many services out there trying to provide information to you. searching wisely with a search service like google can lead you to records or info you would not have found otherwise. (Here's a tutorial on how to use google to help with family history If you know basic google searching skip to the 2nd lesson)

Some kind of tutorial/video here are many free online

Some kind of DNA service (These are usually NOT free. A great idea especially if you have a close dead end within 5-10 generations. It is the best use of money for actual results which will yield for sure ONLY facts if you choose one with a built in family tree/family finder application so much the better)

If you are looking for software or a web service to help you keep track of your family tree Any of These should do nicely.

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