The UK is a member country of the United States’ Visa Waiver Programme (VWP). VWP member countries’ citizens may travel to the US for business or pleasure for a period of less than 90 days without applying for a visa (which is a process involving several steps and that usually takes some time).
VWP travellers, including children, require individual, machine-readable passports. A machine-readable passport can be identified by the presence of two lines of text as letters, numbers and “<”s, printed at the foot of the personal identification page at the back of the passport.
Any full passport issued, renewed or extended between 26 October 2005 and 25 October 2006 must contain a digital photograph.
Any full passport issued, renewed or extended after 26 October 2006 must also include an integrated circuit chip capable of storing the biographic information from the data page, a digitized photograph and other biometric information.
Temporary and emergency passports are exempt from digital photo and electronic chip requirements, but must be machine-readable.
Failure to determine that your passport qualifies for the VWP may result in you being denied boarding by your airline. 
Travel to the US under the VWP will be subject to eligibility being granted by an application under the Electronic System for Travel Authorization (ESTA). An ESTA will also be required in order to transit the United States. If you are a citizen of a VWP country you will need an ESTA, regardless of the country of departure for your journey to the US.
The ESTA application is a web-only system. A third party, such as a relative or travel agent, may submit an ESTA application on your behalf, but you are still legally responsible for the answers submitted. You should apply for an ESTA via the website. The response should be almost immediate. You are highly recommended to apply for your ESTA as far in advance as possible, because if you are for any reason denied an ESTA you will then need to apply for a visa. The ESTA currently costs $14.
An ESTA is valid, unless revoked, for multiple travel to the US for two years or until your passport expires. It is particular to the passport mentioned in the application, so a change of passport means a new ESTA application. Amendments to destination addresses or itineraries, for your original trip or for future trips, can easily be made via the website after your ESTA has been approved.
An ESTA does not guarantee your entry to the United States, which remains subject to the usual inspection by customs/immigration officials on your arrival.
You can find out more information about USA entry requirements at the Government Services and Information website
Many governments now impose extremely strict rules, regulations and laws on what may and may not be included in your carry-on (cabin) baggage on airlines. In general it is safe to assume that nothing that might remotely be considered a weapon will be allowed in the cabin and that this will usually include any kind of knife or sharp implement – right down to penknives, knitting needles or even tweezers.
In addition, many countries now also have stringent rules on what liquids are allowed in hand baggage and this particularly has implications for anyone carrying vital medication or those travelling with babies.
It is highly recommended that you check with your airline for details of what it will and will not accept onto its aircraft, both well before and just prior to travelling. 
See US Customs and Border Protection for full details of all prohibited items.