What you need.
A hardback notebook of reasonable size. Try to avoid loose papers since they rapidly become disorganised.
A pencil, sharpener, eraser and ruler - no pens are allowed in record offices.
A camera is useful in cemeteries and when visiting relatives who have documents/photographs to copy.
A tape recorder is useful in cemeteries and when talking to elderly relatives.
To keep your records, you will either need a folder or large notebook or a computer with suitable software.
Personal Ancestry File version 5 (PAF5) is recommended and can be downloaded free at http://www.familysearch.org
A connection to the Internet is extremely valuable, both as a source of information and for exchange of information with the people already searching your lines - you will find them.

What does it cost?
If you employ a professional, genealogist then expect to pay £200 and more.
You can pay for someone to search the records for you. Professional record searchers charge from £10 to £70 per hour.
If you buy certificates, then these will cost you £11.00 each (£27.00 if you want them in a hurry).
If, after failing to find a parish register or transcript elsewhere, you have to search the parish registers at a church then the Vicar is entitled to charge you 30p plus 15p per year searched. Remember church vestries are cold and sometimes damp and vicars can stand over you impatiently.
If you ask for a microfilm/microfiche to be ordered through your local branch of The Church of Jesus Christ of Latter-Day Saints, then this will cost you about £5 per film/fiche.
Travelling expenses need to be borne in mind - if you have to cross the Atlantic, or travel across country, these can be considerable.
Beware of your family name and heraldic shield of the type "send £50 and we will send you… " type. For the most part, these are inaccurate and a waste of money.

Getting Started
Make out a family tree of your known relatives as far back as you know. This helps to give you a clear idea of what you need to find out and who in your family you can find this out from.

Remember, you are descended from both your father and mother.

You have two parents
Four grand parents
Eight great grandparents
Sixteen great-great grandparents
Thirty-two great, great, great, grandparents (3g grandparents)
Sixty-four 4g grandparents
One hundred twenty-eight 5g grandparents and so on…
By the time you have gone back ten generations, you will be looking for 1,024 ancestors in this tenth generation.
An average woman can have children (legally) between the age of 16 and 48.
Children above age 55 and below 13 are impossible. (OK, we know you can have children at a much later age now but this wasn't available to our ancestors.)
This gives 34 years of child bearing age on average, 42 years max.

If we assume 32 years between generations, then we get this:
Generations Back
Number of ancestors of a child born in 2000
Approximate date of parents birth
Monarch
1
2
1968
 Queen Elizabeth II 
2
4
1936
 George 
3
8
1904
 Edward VII
4
16
1872
 Victoria
5
32
1840
 Victoria
6
64
1808
 George III
7
128
1776
 George III
8
256
1744
 George II
9
512
1712
 Queen Anne
10
1,024
1680
 Charles II
11
2,048
1648
 Charles I
12
4,096
1616
 James I
13
8,192
1584
 Queen Elizabeth I
14
16,384
1552
 Edward VI
By 1552 you will have had to search out 32,766 ancestors.
If however you have 25 years between generations then by 1550 you would have had 18 generations and 524,287 ancestors to find. With 16 years between generations, then by 1550, you would have 27 generations and 268,435,440 in the 27th generation alone - more than the population of the world at that time!

What next?

Have a really good look around at home for any of the following:

All of these sources can give you valuable clues. Take for instance, this bookplate from a book owned by my grandfather, Frederick George Chapman:
To Freddie on your fourteenth birthday, 19 March 1907, from your loving Aunt Esther
This inscription gives me my grandfather's date of birth and tells me, either his father or his mother had a sister (possibly sister-in-law) called Esther. If you're lucky, you many find dates on the back of photographs, post cards often contain dates - check the post mark.

Next, write down what family traditions you know. At this point, consider talking to elderly relations and making a tape recording of the interview. Often, these relatives are a mine of information. They will often know of relations unknown to you and who you can talk to and get information or records from. Check to see if they have any items from the above list. Don't forget to ask questions like:

Family traditions can tell you a lot but, beware, often they may not be very accurate. In my own family we had the following traditions
An ancestor worked in a watermill in Durham City - true, Richard Wilson Chapman was described as a Miller Journeyman at Durham on his son's birth certificate in 1858

An ancestor was the fireman on the train which was involved in the Tay bridge disaster - false but, he was a railway porter and may have seen the train off.

The family owned Headlam Hall and ran a school there - John Chapman rented Headlam Hall and ran a school there in 1805.

The family was rich and were ruined when a Glasgow bank failed - true, My ancestor John Marshall, a mill owner in Kirkaldy, Fifeshire, lost so much money they had to flee to England to avoid creditors.

The family fortune was held in Chancery - partly true, my 1st cousin 5 times removed, Rev. Richard Thomas Wilson Taylor, Rector of St. Mewan in the County of Cornwall left money in trust to the children of his mother's brother, Richard Wilson of Kirkby Stephen, Westmoreland for his descendants. One of these children was my 3rd Great Grandmother Sarah Wilson who married John Robinson Chapman in 1818 at Kirkby Stephen.

The family owned the Olwin Estate - true but the name was miss-spelt, At the time of his death in 1849 my 4th great-grandfather John Chapman owned Alwent Hall Estate (near Gainford, Durham).

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