Start with yourself and work back, documenting everything as you go.
First thing, get as much info from living family as possible, particularly your senior members. Tape them if they will let you. It might turn out they are confused on some things but what might seem to be insignificant story telling might turn out to be very significant.
Find out if any family has any old family bibles. Ask to see and make copies of birth, marriage and death certificates. Also depending on the religious faith, baptismal, first communion, confirmation and marriage certificates can contain vital information.
People involved in genealogy research do not post information about living people in any public forums like the internet as it can be an invasion of privacy and can lead to identity theft.
Go to your public library and find out what all they have in the genealogy section. They might have a subscription to Ancestry.Com which has lots of records and seems to be getting more all the time. They have all the U.S. censuses through 1930. The 1940 and later are not available to the public yet. They have U.K. censuses also.
Just don't take as absolute fact everything you see in their family trees or family trees on ANY website, free or paid. The information is user submitted and mostly not documented or poorly documented. You might see different information from different subscribers on the same people, then you will see repeatedly the same info from the different subscribers on the same people. That is no guarantee at all it is correct. A lot of people copy without verifying. Use the information as CLUES as to where to get the documemtation.
A Family History Center at a Latter Day Saints(Mormon) Church has records on people all over the world, not just Mormons.
You need to call or vist their free website, FamilySearch.org and find out their hours for the general public. In Salt Lake City, they have the world's largest genealogical collection. Their Family History Centers can order microfilm for you to view at a nominal fee.
I have never had them to try and convert me or send their missionaries by to ring my doorbell. I haven't heard of them doing that to anyones else that has used their resources. They are just very nice and helpful.
You will need to order vital records. In the U.S., each state has its own laws about who, when and where a person can obtain vital records on another. States are clamping down on birth certificates due to the risk of idenitity theft. In Texas, if you were not immediate family,it use to be 50 years after someone was born before you could get a birth certificate on another. Now it is 75 years.
Also each state started getting vital info at different times. Many did not start recording birth and death records until the first part of the 20th century. Once they started a lot of people who were born at home or died at home did not get recorded.
Courthouse records like wills, deeds etc can be very valuable.
You mention church and yes, church records, depending on the faith, are very important sources before the states began recording birth and death records.
Cyndi'slist.com has a multitude of websites that can be helpful in obtaining information.